Update explanation of modular exponentiation

Updated copyright year from 2022 to 2026 in the license section.

.github/workflows/on-file-change.yml

@@ -0,0 +1,34 @@
+name: Update README from Pytudes
+
+on:
+  push:
+    paths:
+      - 'py/pytudes.py'
+
+jobs:
+  build-and-update:
+    runs-on: ubuntu-latest
+    # Added permissions to allow the bot to write to the repo
+    permissions:
+      contents: write
+
+    steps:
+      - name: Checkout repository
+        uses: actions/checkout@v4
+
+      - name: Set up Python
+        uses: actions/setup-python@v4
+        with:
+          python-version: '3.10'
+
+      - name: Run pytudes.py
+        run: python py/pytudes.py
+
+      - name: Commit and push if README changed
+        run: |
+          git config --local user.email "github-actions[bot]@users.noreply.github.com"
+          git config --local user.name "github-actions[bot]"
+          git add README.md
+          # The || exit 0 prevents the workflow from failing if there are no changes
+          git commit -m "docs: auto-update README.md via pytudes.py" || exit 0
+          git push

README.md

@@ -1,6 +1,6 @@
 
 <div align="right" style="text-align:right"><i>Peter Norvig
-<br><a href="https://github.com/norvig/pytudes/blob/main/LICENSE">MIT License</a><br>2015-2022</i></div>
+<br><a href="https://github.com/norvig/pytudes/blob/main/LICENSE">MIT License</a><br>2015-2026</i></div>
 
 # pytudes
 
@@ -13,7 +13,6 @@ This project contains ***pytudes***—Python programs, usually short, for perfec
 
 To continue the musical analogy, some people think of programming like [Spotify](http://spotify.com): they want to know how to install the app, find a good playlist, and hit the "play" button; after that they don't want to think about it. There are plenty of other tutorials that will tell you how to do the equivalent of that for various programming tasks—this one won't help. But if you think of programming like playing the piano—a craft that can take [years](https://norvig.com/21-days.html) to perfect—then I hope this collection can help.
 
-
 # Index of Jupyter (IPython) Notebooks
 
 For each notebook you can hover on the title to see a description, or click the title to view on github, or click one of the letters in the left column to launch the notebook on 
@@ -27,19 +26,16 @@ For each notebook you can hover on the title to see a description, or click the
 
 |Run|Year|New|
 |---|---|---|
+| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/TruncatablePrimes.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FTruncatablePrimes.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FTruncatablePrimes.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/TruncatablePrimes.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/TruncatablePrimes.ipynb) | <u>2026</u> | <a href="ipynb/TruncatablePrimes.ipynb" title="Prime numbers where you can remove digits and still get primes.">Truncatable Primes</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Advent-2025.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FAdvent-2025.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FAdvent-2025.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Advent-2025.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Advent-2025.ipynb) | 2025 | <a href="ipynb/Advent-2025.ipynb" title="Puzzle site with a coding puzzle for 12 days of Christmas, December 2025">Advent of Code 2025</a> |
-| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Advent-2025-AI.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FAdvent-2025-AI.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FAdvent-2025-AI.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Advent-2025-AI.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Advent-2025-AI.ipynb) | 2025 | <a href="ipynb/Advent-2025-AI.ipynb" title="Using large language coding models to solve AoC puzzles">Advent of Code 2025: AI LLM edition</a> |
-| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Advent-2024.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FAdvent-2024.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FAdvent-2024.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Advent-2024.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Advent-2024.ipynb) | <u>2024</u> | <a href="ipynb/Advent-2024.ipynb" title="Puzzle site with a coding puzzle each day of Advent, December 2024">Advent of Code 2024</a> |
-| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Paint.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FPaint.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FPaint.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Paint.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Paint.ipynb) | <u>2024</u> | <a href="ipynb/Paint.ipynb" title="What is the average cluster size of a random grid of colored squares?">Counting Cluster Sizes in Paint by Numbers</a> |
-| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/CherylMind.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FCherylMind.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FCherylMind.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/CherylMind.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/CherylMind.ipynb) | <u>2024</u> | <a href="ipynb/CherylMind.ipynb" title="Do LLMs have enough theory of mind to solve the Cheryl's Birthday puzzle?">LLMs, Theory of Mind, and Cheryl's Birthday</a> |
-| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/NumberBracelets.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FNumberBracelets.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FNumberBracelets.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/NumberBracelets.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/NumberBracelets.ipynb) | <u>2024</u> | <a href="ipynb/NumberBracelets.ipynb" title="A game involving numbered beads on a circular bracelet.">Number Bracelets Game</a> |
-| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Overtime.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FOvertime.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FOvertime.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Overtime.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Overtime.ipynb) | <u>2024</u> | <a href="ipynb/Overtime.ipynb" title="In American Football, which team has the advantage in overtime?">Overtime in American Football</a> |
-| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Stubborn.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FStubborn.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FStubborn.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Stubborn.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Stubborn.ipynb) | <u>2024</u> | <a href="ipynb/Stubborn.ipynb" title="Any number ending in 5 has a square that also ends in 5. What other endings are like this?">Stubborn number endings</a> |
-| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Triplets.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FTriplets.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FTriplets.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Triplets.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Triplets.ipynb) | <u>2024</u> | <a href="ipynb/Triplets.ipynb" title="LLMs do better at producing a program to solve this puzzle than they do at solving it directly">The Languages of English, Math, and Programming</a> |
-| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Advent-2023.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FAdvent-2023.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FAdvent-2023.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Advent-2023.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Advent-2023.ipynb) | 2023 | <a href="ipynb/Advent-2023.ipynb" title="Puzzle site with a coding puzzle each day of Advent, December 2023">Advent of Code 2023</a> |
-| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/DocstringFixpoint.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FDocstringFixpoint.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FDocstringFixpoint.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/DocstringFixpoint.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/DocstringFixpoint.ipynb) | 2023 | <a href="ipynb/DocstringFixpoint.ipynb" title="An approach to writing code and docstrings that go together.">Docstring Fixpoint Theory</a> |
-| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/OneLetterOff.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FOneLetterOff.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FOneLetterOff.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/OneLetterOff.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/OneLetterOff.ipynb) | 2023 | <a href="ipynb/OneLetterOff.ipynb" title="Word game; use of a large language model to generate clues.">One Letter Off</a> |
-| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Diamonds.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FDiamonds.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FDiamonds.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Diamonds.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Diamonds.ipynb) | 2023 | <a href="ipynb/Diamonds.ipynb" title="Finding an optimal strategy for buying bags with unknown numbers of diamonds.">The Diamond Game: A Probability Puzzle</a> |
+| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Advent-2025-AI.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FAdvent-2025-AI.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FAdvent-2025-AI.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Advent-2025-AI.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Advent-2025-AI.ipynb) | 2025 | <a href="ipynb/Advent-2025-AI.ipynb" title="Using large language coding models to solve AoC puzzles">Advent of Code 2025: AI LLM Edition</a> |
+| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Advent-2024.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FAdvent-2024.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FAdvent-2024.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Advent-2024.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Advent-2024.ipynb) | 2024 | <a href="ipynb/Advent-2024.ipynb" title="Puzzle site with a coding puzzle each day of Advent, December 2024">Advent of Code 2024</a> |
+| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Paint.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FPaint.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FPaint.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Paint.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Paint.ipynb) | 2024 | <a href="ipynb/Paint.ipynb" title="What is the average cluster size of a random grid of colored squares?">Counting Cluster Sizes in Paint by Numbers</a> |
+| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/CherylMind.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FCherylMind.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FCherylMind.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/CherylMind.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/CherylMind.ipynb) | 2024 | <a href="ipynb/CherylMind.ipynb" title="Do LLMs have enough theory of mind to solve the Cheryl's Birthday puzzle?">LLMs, Theory of Mind, and Cheryl's Birthday</a> |
+| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/NumberBracelets.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FNumberBracelets.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FNumberBracelets.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/NumberBracelets.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/NumberBracelets.ipynb) | 2024 | <a href="ipynb/NumberBracelets.ipynb" title="A game involving numbered beads on a circular bracelet.">Number Bracelets Game</a> |
+| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Overtime.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FOvertime.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FOvertime.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Overtime.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Overtime.ipynb) | 2024 | <a href="ipynb/Overtime.ipynb" title="In American Football, which team has the advantage in overtime?">Overtime in American Football</a> |
+| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Stubborn.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FStubborn.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FStubborn.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Stubborn.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Stubborn.ipynb) | 2024 | <a href="ipynb/Stubborn.ipynb" title="Any number ending in 5 has a square that also ends in 5. What other endings are like this?">Stubborn number endings</a> |
+| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Triplets.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FTriplets.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FTriplets.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Triplets.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Triplets.ipynb) | 2024 | <a href="ipynb/Triplets.ipynb" title="LLMs do better at producing a program to solve this puzzle than they do at solving it directly">The Languages of English, Math, and Programming</a> |
 
 
 |Run|Year|Programming Examples|
@@ -52,7 +48,7 @@ For each notebook you can hover on the title to see a description, or click the
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Sierpinski.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FSierpinski.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FSierpinski.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Sierpinski.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Sierpinski.ipynb) | 2019 | <a href="ipynb/Sierpinski.ipynb" title="A surprising appearance of the Sierpinski triangle in a random walk">Chaos with Triangles</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Life.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FLife.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FLife.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Life.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Life.ipynb) | 2017 | <a href="ipynb/Life.ipynb" title="The cellular automata zero-player game">Conway's Game of Life</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Maze.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FMaze.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FMaze.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Maze.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Maze.ipynb) | 2020 | <a href="ipynb/Maze.ipynb" title="Make a maze by generating a random tree superimposed on a grid and solve it">Generating and Solving Mazes</a> |
-| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Triplets.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FTriplets.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FTriplets.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Triplets.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Triplets.ipynb) | <u>2024</u> | <a href="ipynb/Triplets.ipynb" title="LLMs do better at producing a program to solve this puzzle than they do at solving it directly">The Languages of English, Math, and Programming</a> |
+| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Triplets.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FTriplets.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FTriplets.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Triplets.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Triplets.ipynb) | 2024 | <a href="ipynb/Triplets.ipynb" title="LLMs do better at producing a program to solve this puzzle than they do at solving it directly">The Languages of English, Math, and Programming</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Konane.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FKonane.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FKonane.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Konane.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Konane.ipynb) | 2021 | <a href="ipynb/Konane.ipynb" title="Solving the game of Konane (Hawaiian checkers).">Mel's Konane Board</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/PhotoFocalLengths.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FPhotoFocalLengths.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FPhotoFocalLengths.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/PhotoFocalLengths.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/PhotoFocalLengths.ipynb) | 2020 | <a href="ipynb/PhotoFocalLengths.ipynb" title="Generate charts of what focal lengths were used on a photo trip">Photo Focal Lengths</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Pickleball.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FPickleball.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FPickleball.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Pickleball.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Pickleball.ipynb) | 2018 | <a href="ipynb/Pickleball.ipynb" title="Scheduling a doubles tournament fairly and efficiently">Pickleball Tournament</a> |
@@ -63,9 +59,9 @@ For each notebook you can hover on the title to see a description, or click the
 
 |Run|Year|Advent of Code|
 |---|---|---|
-| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Advent-2025-AI.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FAdvent-2025-AI.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FAdvent-2025-AI.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Advent-2025-AI.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Advent-2025-AI.ipynb) | 2025 | <a href="ipynb/Advent-2025-AI.ipynb" title="Using large language coding models to solve AoC puzzles">AoC 2025: AI LLM edition</a> |
+| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Advent-2025-AI.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FAdvent-2025-AI.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FAdvent-2025-AI.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Advent-2025-AI.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Advent-2025-AI.ipynb) | 2025 | <a href="ipynb/Advent-2025-AI.ipynb" title="Using large language coding models to solve AoC puzzles">Advent of Code 2025: AI LLM Edition</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Advent-2025.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FAdvent-2025.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FAdvent-2025.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Advent-2025.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Advent-2025.ipynb) | 2025 | <a href="ipynb/Advent-2025.ipynb" title="Puzzle site with a coding puzzle for 12 days of Christmas, December 2025">Advent of Code 2025</a> |
-| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Advent-2024.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FAdvent-2024.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FAdvent-2024.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Advent-2024.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Advent-2024.ipynb) | <u>2024</u> | <a href="ipynb/Advent-2024.ipynb" title="Puzzle site with a coding puzzle each day of Advent, December 2024">Advent of Code 2024</a> |
+| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Advent-2024.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FAdvent-2024.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FAdvent-2024.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Advent-2024.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Advent-2024.ipynb) | 2024 | <a href="ipynb/Advent-2024.ipynb" title="Puzzle site with a coding puzzle each day of Advent, December 2024">Advent of Code 2024</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Advent-2023.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FAdvent-2023.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FAdvent-2023.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Advent-2023.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Advent-2023.ipynb) | 2023 | <a href="ipynb/Advent-2023.ipynb" title="Puzzle site with a coding puzzle each day of Advent, December 2023">Advent of Code 2023</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Advent-2022.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FAdvent-2022.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FAdvent-2022.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Advent-2022.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Advent-2022.ipynb) | 2022 | <a href="ipynb/Advent-2022.ipynb" title="Puzzle site with a coding puzzle each day of Advent, December 2022">Advent of Code 2022</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Advent-2021.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FAdvent-2021.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FAdvent-2021.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Advent-2021.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Advent-2021.ipynb) | 2021 | <a href="ipynb/Advent-2021.ipynb" title="Puzzle site with a coding puzzle each day of Advent, December 2021">Advent of Code 2021</a> |
@@ -86,7 +82,7 @@ For each notebook you can hover on the title to see a description, or click the
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Coin%20Flip.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FCoin%20Flip.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FCoin%20Flip.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Coin%20Flip.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Coin%20Flip.ipynb) | 2019 | <a href="ipynb/Coin%20Flip.ipynb" title="How to beat the Devil at his own game">The Devil and the Coin Flip Game</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Dice%20Baseball.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FDice%20Baseball.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FDice%20Baseball.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Dice%20Baseball.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Dice%20Baseball.ipynb) | 2020 | <a href="ipynb/Dice%20Baseball.ipynb" title="Simulating baseball games">Dice Baseball</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Economics.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FEconomics.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FEconomics.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Economics.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Economics.ipynb) | 2018 | <a href="ipynb/Economics.ipynb" title="A simulation of a simple economic game">Economics Simulation</a> |
-| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Overtime.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FOvertime.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FOvertime.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Overtime.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Overtime.ipynb) | <u>2024</u> | <a href="ipynb/Overtime.ipynb" title="In American Football, which team has the advantage in overtime?">Overtime in American Football</a> |
+| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Overtime.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FOvertime.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FOvertime.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Overtime.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Overtime.ipynb) | 2024 | <a href="ipynb/Overtime.ipynb" title="In American Football, which team has the advantage in overtime?">Overtime in American Football</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/poker.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2Fpoker.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2Fpoker.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/poker.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/poker.ipynb) | 2012 | <a href="ipynb/poker.ipynb" title="How do we decide which poker hand wins? Several variants of poker are considered">Poker Hand Ranking</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/risk.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2Frisk.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2Frisk.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/risk.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/risk.ipynb) | 2020 | <a href="ipynb/risk.ipynb" title="Determining who is likely to win an interminably long game of Risk">The Unfinished Game .... of Risk</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/WWW.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FWWW.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FWWW.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/WWW.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/WWW.ipynb) | 2019 | <a href="ipynb/WWW.ipynb" title="Computing the probability of winning the NBA title, for my home town Warriors, or any other team">WWW: Who Will Win (NBA Title)?</a> |
@@ -94,24 +90,24 @@ For each notebook you can hover on the title to see a description, or click the
 
 |Run|Year|Logic and Number/Counting Puzzles|
 |---|---|---|
-| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Paint.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FPaint.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FPaint.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Paint.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Paint.ipynb) | <u>2024</u> | <a href="ipynb/Paint.ipynb" title="What is the average cluster size of a random grid of colored squares?">Counting Cluster Sizes in Paint by Numbers</a> |
+| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Paint.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FPaint.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FPaint.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Paint.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Paint.ipynb) | 2024 | <a href="ipynb/Paint.ipynb" title="What is the average cluster size of a random grid of colored squares?">Counting Cluster Sizes in Paint by Numbers</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Cryptarithmetic.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FCryptarithmetic.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FCryptarithmetic.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Cryptarithmetic.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Cryptarithmetic.ipynb) | 2014 | <a href="ipynb/Cryptarithmetic.ipynb" title="Substitute digits for letters and make NUM + BER = PLAY">Cryptarithmetic</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Euler's%20Conjecture.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FEuler's%20Conjecture.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FEuler's%20Conjecture.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Euler's%20Conjecture.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Euler's%20Conjecture.ipynb) | 2018 | <a href="ipynb/Euler's%20Conjecture.ipynb" title="Solving a 200-year-old puzzle by finding integers that satisfy a<sup>5</sup> + b<sup>5</sup> + c<sup>5</sup> + d<sup>5</sup> = e<sup>5</sup>">Euler's Sum of Powers Conjecture</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Countdown.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FCountdown.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FCountdown.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Countdown.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Countdown.ipynb) | 2020 | <a href="ipynb/Countdown.ipynb" title="Solving the equation 10 _ 9 _ 8 _ 7 _ 6 _ 5 _ 4 _ 3 _ 2 _ 1 = 2016. Originally from an Alex Bellos puzzle">Four 4s, Five 5s, and Countdowns</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/How%20To%20Count%20Things.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FHow%20To%20Count%20Things.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FHow%20To%20Count%20Things.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/How%20To%20Count%20Things.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/How%20To%20Count%20Things.ipynb) | 2020 | <a href="ipynb/How%20To%20Count%20Things.ipynb" title="Combinatorial math: how to count how many things there are, when there are a lot of them">How to Count Things</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/KenKen.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FKenKen.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FKenKen.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/KenKen.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/KenKen.ipynb) | 2021 | <a href="ipynb/KenKen.ipynb" title="A Sudoku-like puzzle, but with arithmetic.">KenKen (Sudoku-like Puzzle)</a> |
-| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/NumberBracelets.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FNumberBracelets.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FNumberBracelets.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/NumberBracelets.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/NumberBracelets.ipynb) | <u>2024</u> | <a href="ipynb/NumberBracelets.ipynb" title="A game involving numbered beads on a circular bracelet.">Number Bracelets Game</a> |
+| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/NumberBracelets.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FNumberBracelets.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FNumberBracelets.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/NumberBracelets.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/NumberBracelets.ipynb) | 2024 | <a href="ipynb/NumberBracelets.ipynb" title="A game involving numbered beads on a circular bracelet.">Number Bracelets Game</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Socks.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FSocks.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FSocks.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Socks.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Socks.ipynb) | 2019 | <a href="ipynb/Socks.ipynb" title="What is the probability that you will be able to pair up socks as you randomly pull them out of the dryer?">Pairing Socks</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Sicherman%20Dice.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FSicherman%20Dice.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FSicherman%20Dice.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Sicherman%20Dice.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Sicherman%20Dice.ipynb) | 2018 | <a href="ipynb/Sicherman%20Dice.ipynb" title="Find a pair of dice that is like a regular pair of dice, only different">Sicherman Dice</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Golomb-Puzzle.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FGolomb-Puzzle.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FGolomb-Puzzle.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Golomb-Puzzle.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Golomb-Puzzle.ipynb) | 2014 | <a href="ipynb/Golomb-Puzzle.ipynb" title="A Puzzle involving placing rectangles of different sizes inside a square">Sol Golomb's Rectangle Puzzle</a> |
-| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Stubborn.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FStubborn.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FStubborn.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Stubborn.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Stubborn.ipynb) | <u>2024</u> | <a href="ipynb/Stubborn.ipynb" title="Any number ending in 5 has a square that also ends in 5. What other endings are like this?">Stubborn number endings</a> |
+| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Stubborn.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FStubborn.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FStubborn.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Stubborn.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Stubborn.ipynb) | 2024 | <a href="ipynb/Stubborn.ipynb" title="Any number ending in 5 has a square that also ends in 5. What other endings are like this?">Stubborn number endings</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/StarBattle.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FStarBattle.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FStarBattle.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/StarBattle.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/StarBattle.ipynb) | 2021 | <a href="ipynb/StarBattle.ipynb" title="Fill-in-the-grid puzzle similar to Sudoku">Star Battle (Sudoku-like Puzzle)</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Sudoku.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FSudoku.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FSudoku.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Sudoku.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Sudoku.ipynb) | 2006 | <a href="ipynb/Sudoku.ipynb" title="Classic fill-in-the-grid puzzle">Sudoku</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/SudokuJava.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FSudokuJava.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FSudokuJava.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/SudokuJava.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/SudokuJava.ipynb) | 2021 | <a href="ipynb/SudokuJava.ipynb" title="A version of the Sudoku solver using parallel threads and other optimizations">Sudoku: 100,000 puzzles/second in Java</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/SquareSum.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FSquareSum.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FSquareSum.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/SquareSum.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/SquareSum.ipynb) | 2020 | <a href="ipynb/SquareSum.ipynb" title="Place the numbers from 1 to n in a chain (or a circle) such that adjacent pairs sum to a perfect square">Square Sum Puzzle</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Cheryl.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FCheryl.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FCheryl.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Cheryl.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Cheryl.ipynb) | 2020 | <a href="ipynb/Cheryl.ipynb" title="Solving the *Cheryl's Birthday* logic puzzle">When is Cheryl's Birthday?</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Cheryl-and-Eve.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FCheryl-and-Eve.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FCheryl-and-Eve.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Cheryl-and-Eve.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Cheryl-and-Eve.ipynb) | 2015 | <a href="ipynb/Cheryl-and-Eve.ipynb" title="Inventing new puzzles in the Style of Cheryl's Birthday">When Cheryl Met Eve: A Birthday Story</a> |
-| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/CherylMind.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FCherylMind.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FCherylMind.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/CherylMind.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/CherylMind.ipynb) | <u>2024</u> | <a href="ipynb/CherylMind.ipynb" title="Do LLMs have enough theory of mind to solve the Cheryl's Birthday puzzle?">LLMs, Theory of Mind, and Cheryl's Birthday</a> |
+| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/CherylMind.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FCherylMind.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FCherylMind.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/CherylMind.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/CherylMind.ipynb) | 2024 | <a href="ipynb/CherylMind.ipynb" title="Do LLMs have enough theory of mind to solve the Cheryl's Birthday puzzle?">LLMs, Theory of Mind, and Cheryl's Birthday</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/xkcd1313.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2Fxkcd1313.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2Fxkcd1313.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/xkcd1313.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/xkcd1313.ipynb) | 2015 | <a href="ipynb/xkcd1313.ipynb" title="Find the smallest regular expression; inspired by Randall Munroe">xkcd 1313: Regex Golf</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/xkcd1313-part2.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2Fxkcd1313-part2.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2Fxkcd1313-part2.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/xkcd1313-part2.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/xkcd1313-part2.ipynb) | 2015 | <a href="ipynb/xkcd1313-part2.ipynb" title="Regex Golf: better, faster, funner (with Stefan Pochmann)">xkcd 1313: Regex Golf (Part 2: Infinite Problems)</a> |
 
@@ -146,7 +142,7 @@ For each notebook you can hover on the title to see a description, or click the
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/RiddlerLottery.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FRiddlerLottery.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FRiddlerLottery.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/RiddlerLottery.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/RiddlerLottery.ipynb) | 2019 | <a href="ipynb/RiddlerLottery.ipynb" title="Can you find what lottery number tickets these five friends picked?">Lottery</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/NightKing.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FNightKing.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FNightKing.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/NightKing.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/NightKing.ipynb) | 2019 | <a href="ipynb/NightKing.ipynb" title="A battle between the army of the dead and the army of the living">How Many Soldiers to Beat the Night King?</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Mean%20Misanthrope%20Density.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FMean%20Misanthrope%20Density.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FMean%20Misanthrope%20Density.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Mean%20Misanthrope%20Density.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Mean%20Misanthrope%20Density.ipynb) | 2017 | <a href="ipynb/Mean%20Misanthrope%20Density.ipynb" title="How crowded will this neighborhood be, if nobody wants to live next door to anyone else?">Misanthropic Neighbors</a> |
-| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Orderable%20Cards.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FOrderable%20Cards.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FOrderable%20Cards.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Orderable%20Cards.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Orderable%20Cards.ipynb) | 2018 | <a href="ipynb/Orderable%20Cards.ipynb" title="Can you get your hand of cards into a nice order with just one move?">Properly Ordered Card Hands</a> |
+| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Orderable%20Cards.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FOrderable%20Cards.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FOrderable%20Cards.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Orderable%20Cards.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Orderable%20Cards.ipynb) | 2018 | <a href="ipynb/Orderable%20Cards.ipynb" title="Can you get your hand of cards into a nice order with just one move?">Properly Organized Card Hands</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/RaceTrack.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FRaceTrack.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FRaceTrack.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/RaceTrack.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/RaceTrack.ipynb) | 2021 | <a href="ipynb/RaceTrack.ipynb" title="Race virtual cars around a circular track defined on a grid of points.">Race Track</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/SplitStates.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FSplitStates.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FSplitStates.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/SplitStates.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/SplitStates.ipynb) | 2021 | <a href="ipynb/SplitStates.ipynb" title="Split the US states into two near-halves by area.">Split the States</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/TourDe538.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FTourDe538.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FTourDe538.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/TourDe538.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/TourDe538.ipynb) | 2020 | <a href="ipynb/TourDe538.ipynb" title="Solve a puzzle involving the best pace for a bicycle race.">Tour de 538</a> |
@@ -160,9 +156,10 @@ For each notebook you can hover on the title to see a description, or click the
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Convex%20Hull.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FConvex%20Hull.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FConvex%20Hull.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Convex%20Hull.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Convex%20Hull.ipynb) | 2017 | <a href="ipynb/Convex%20Hull.ipynb" title="A classic Computer Science Algorithm">Convex Hull Problem</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/DocstringFixpoint.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FDocstringFixpoint.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FDocstringFixpoint.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/DocstringFixpoint.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/DocstringFixpoint.ipynb) | 2023 | <a href="ipynb/DocstringFixpoint.ipynb" title="An approach to writing code and docstrings that go together.">Docstring Fixpoint Theory</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/StableMatching.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FStableMatching.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FStableMatching.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/StableMatching.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/StableMatching.ipynb) | 2020 | <a href="ipynb/StableMatching.ipynb" title="What is the best way to pair up two groups with each other, obeying preferences?">Stable Matching Problem</a> |
-| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Differentiation.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FDifferentiation.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FDifferentiation.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Differentiation.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Differentiation.ipynb) | 2017 | <a href="ipynb/Differentiation.ipynb" title="A computer algebra system that, including symbolic differentiation">Symbolic Algebra, Simplification, and Differentiation</a> |
+| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Differentiation.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FDifferentiation.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FDifferentiation.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Differentiation.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Differentiation.ipynb) | 2017 | <a href="ipynb/Differentiation.ipynb" title="A computer algebra system, including symbolic differentiation">Symbolic Algebra, Simplification, and Differentiation</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Snobol.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FSnobol.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FSnobol.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Snobol.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/Snobol.ipynb) | 2017 | <a href="ipynb/Snobol.ipynb" title="As a student, did you ever get a bad grade on a programming assignment?">Snobol: Bad Grade, Good Experience</a> |
 | [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/TSP.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FTSP.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FTSP.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/TSP.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/TSP.ipynb) | 2018 | <a href="ipynb/TSP.ipynb" title="Another of the classics">Traveling Salesperson Problem</a> |
+| [C](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/TruncatablePrimes.ipynb) [D](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FTruncatablePrimes.ipynb) [M](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FTruncatablePrimes.ipynb) [N](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/TruncatablePrimes.ipynb) [S](https://studiolab.sagemaker.aws/import/github/norvig/pytudes/blob/main/ipynb/TruncatablePrimes.ipynb) | <u>2026</u> | <a href="ipynb/TruncatablePrimes.ipynb" title="Prime numbers where you can remove digits and still get primes.">Truncatable Primes</a> |
 
 # Index of Python Files
 
@@ -189,9 +186,25 @@ For each notebook you can hover on the title to see a description, or click the
 |[yaptu.py](/py/yaptu.py)|*Yet Another Python Templating Utility*||
 
 # Etudes for Programmers
+
 I got the idea for the *"etudes"* part of the name from
 this [1978 book](https://books.google.com/books/about/Etudes_for_programmers.html?id=u89WAAAAMAAJ)
 by [Charles Wetherell](http://demin.ws/blog/english/2012/08/25/interview-with-charles-wetherell)
-that was very influential to me when I was first learning to program. I still have my copy.
+that was very influential to me when I was first learning to program. I still have my copy, but
+it is now easier to find a [pdf](txt/Etudes.pdf) than a hard copy.
 
 ![](https://images-na.ssl-images-amazon.com/images/I/51ZnZH29dvL._SX394_BO1,204,203,200_.jpg)
+
+# Reviews of pytudes
+
+Here's what some people are saying about `pytudes`:
+- "What I find interesting is how Peter builds bottom-up solutions using low-level utilities... Reading his code is educational." - [Jeremey Howard](https://en.wikipedia.org/wiki/Jeremy_Howard_(entrepreneur)), co-founder of fast.ai and chief scientist at Kaggle
+- "Everything I see from Peter Norvig is just always so incredibly well written and coded." — [Jonathan](https://news.ycombinator.com/user?id=jypepin), [Hacker News](https://news.ycombinator.com/item?id=27379366)
+- "Peter Norvig is my go to recommendation when someone is interested in becoming better at solving day to day problems ... I feel his skill of dividing a problem into small pieces and expressing them in code in a natural way is unparalleled." — [mikevin](https://news.ycombinator.com/user?id=mikevin), [Hacker News](https://news.ycombinator.com/item?id=27379366)
+- "I've never seen Peter Norvig choose anything but the most elegant and perfect data model for the problem at hand." — [spoonjim](https://news.ycombinator.com/user?id=spoonjim), [Hacker News](https://news.ycombinator.com/item?id=27379366)
+- "I just find Norvig's style of "functional Python" lovely in its own way (with noted disregard of Pep8 and other "best practices")" —[raverbashing](https://news.ycombinator.com/user?id=raverbashing), [Hacker News](https://news.ycombinator.com/item?id=25654955)
+- "You should check out Norvig's design of computer programs [course on Udacity](https://imp.i115008.net/c/2331964/788805/11298?u=https://www.udacity.com/course/design-of-computer-programs--cs212) where he uses these kinds of puzzle programs to teach programming design concepts. It is a hard but really rewarding course. — [nafizh](https://news.ycombinator.com/user?id=nafizh), [HN ACademy](https://yahnd.com/academy/r/udacity.com/course/design-of-computer-programs--cs212/)
+- "Often enough I would think of something [a possible improvement[, but if you worked it out in detail there was some less-obvious reason the code was the way it was... All the code is pretty short, and it's not really 'production code', but it's enough to be an education in craftsmanship at every level."
+- [What code samples should programmers read?] "Anything else implemented by Norvig, he's one of the best programmers that I've had the pleasure of reading code from." - [jacquesm](https://news.ycombinator.com/user?id=jacquesm) on [Hacker News](https://news.ycombinator.com/item?id=14487724)
+- "Everything I see from Peter Norvig is just always so incredibly well written and coded. Every year looking at his solutions for advent of code [0] brings just so much learnings. Strongly recommend. - [jyepin](https://news.ycombinator.com/user?id=jypepin) [Hacker News](https://news.ycombinator.com/item?id=27379366)
+- "I feel his skill of dividing a problem into small pieces and expressing them in code in a natural way is unparalleled." - [mikevin](https://news.ycombinator.com/user?id=mikevin) [Hacker News](https://news.ycombinator.com/item?id=27379366)

data/advent2016/input1.txt

@@ -1 +0,0 @@
-R4, R5, L5, L5, L3, R2, R1, R1, L5, R5, R2, L1, L3, L4, R3, L1, L1, R2, R3, R3, R1, L3, L5, R3, R1, L1, R1, R2, L1, L4, L5, R4, R2, L192, R5, L2, R53, R1, L5, R73, R5, L5, R186, L3, L2, R1, R3, L3, L3, R1, L4, L2, R3, L5, R4, R3, R1, L1, R5, R2, R1, R1, R1, R3, R2, L1, R5, R1, L5, R2, L2, L4, R3, L1, R4, L5, R4, R3, L5, L3, R4, R2, L5, L5, R2, R3, R5, R4, R2, R1, L1, L5, L2, L3, L4, L5, L4, L5, L1, R3, R4, R5, R3, L5, L4, L3, L1, L4, R2, R5, R5, R4, L2, L4, R3, R1, L2, R5, L5, R1, R1, L1, L5, L5, L2, L1, R5, R2, L4, L1, R4, R3, L3, R1, R5, L1, L4, R2, L3, R5, R3, R1, L3

data/advent2016/input10.txt

@@ -1,231 +0,0 @@
-value 23 goes to bot 208
-bot 125 gives low to bot 58 and high to bot 57
-value 13 goes to bot 161
-bot 178 gives low to bot 88 and high to bot 172
-value 59 goes to bot 128
-bot 173 gives low to bot 83 and high to bot 202
-bot 189 gives low to bot 35 and high to bot 55
-bot 123 gives low to bot 90 and high to bot 169
-bot 148 gives low to bot 101 and high to bot 134
-bot 36 gives low to bot 78 and high to bot 105
-bot 196 gives low to bot 171 and high to bot 45
-bot 157 gives low to bot 179 and high to bot 87
-bot 124 gives low to bot 25 and high to bot 80
-bot 55 gives low to bot 99 and high to bot 201
-value 17 goes to bot 4
-bot 127 gives low to bot 118 and high to bot 142
-bot 9 gives low to bot 61 and high to bot 198
-bot 71 gives low to bot 86 and high to bot 96
-bot 86 gives low to bot 98 and high to bot 149
-bot 176 gives low to bot 89 and high to bot 171
-bot 38 gives low to bot 107 and high to bot 63
-bot 67 gives low to bot 77 and high to bot 7
-bot 131 gives low to output 6 and high to bot 151
-bot 97 gives low to bot 33 and high to bot 16
-bot 89 gives low to bot 27 and high to bot 36
-bot 29 gives low to bot 185 and high to bot 11
-bot 92 gives low to bot 189 and high to bot 122
-bot 77 gives low to output 7 and high to bot 191
-bot 14 gives low to bot 152 and high to bot 179
-bot 49 gives low to bot 76 and high to bot 64
-value 2 goes to bot 155
-bot 159 gives low to bot 182 and high to bot 49
-bot 129 gives low to bot 141 and high to bot 40
-bot 50 gives low to output 1 and high to bot 47
-bot 93 gives low to output 5 and high to bot 167
-bot 112 gives low to output 13 and high to bot 51
-bot 165 gives low to bot 163 and high to bot 123
-bot 13 gives low to bot 75 and high to bot 74
-bot 141 gives low to bot 178 and high to bot 207
-bot 37 gives low to bot 42 and high to bot 139
-value 31 goes to bot 92
-bot 44 gives low to bot 16 and high to bot 91
-bot 172 gives low to bot 84 and high to bot 27
-bot 39 gives low to bot 44 and high to bot 154
-bot 170 gives low to bot 95 and high to bot 146
-bot 98 gives low to bot 193 and high to bot 17
-bot 4 gives low to bot 26 and high to bot 109
-bot 197 gives low to bot 71 and high to bot 106
-bot 132 gives low to bot 161 and high to bot 181
-bot 54 gives low to bot 156 and high to bot 148
-bot 140 gives low to bot 0 and high to bot 25
-bot 59 gives low to output 10 and high to bot 93
-bot 206 gives low to bot 2 and high to bot 200
-bot 5 gives low to bot 201 and high to bot 173
-bot 81 gives low to bot 24 and high to bot 30
-bot 33 gives low to bot 100 and high to bot 113
-bot 73 gives low to bot 60 and high to bot 129
-bot 43 gives low to output 14 and high to bot 204
-bot 143 gives low to bot 176 and high to bot 196
-bot 182 gives low to bot 70 and high to bot 76
-bot 139 gives low to bot 117 and high to bot 180
-bot 31 gives low to bot 131 and high to bot 137
-bot 179 gives low to bot 31 and high to bot 28
-bot 74 gives low to bot 29 and high to bot 160
-bot 7 gives low to bot 191 and high to bot 21
-bot 83 gives low to bot 165 and high to bot 116
-bot 142 gives low to bot 144 and high to bot 107
-bot 187 gives low to bot 129 and high to bot 68
-value 61 goes to bot 32
-bot 32 gives low to bot 72 and high to bot 53
-bot 53 gives low to bot 121 and high to bot 199
-bot 79 gives low to bot 143 and high to bot 196
-bot 0 gives low to bot 92 and high to bot 194
-bot 8 gives low to bot 56 and high to bot 209
-value 43 goes to bot 72
-bot 95 gives low to output 18 and high to bot 112
-bot 104 gives low to bot 41 and high to bot 185
-bot 198 gives low to bot 103 and high to bot 48
-bot 17 gives low to bot 69 and high to bot 156
-bot 138 gives low to output 0 and high to bot 77
-bot 76 gives low to bot 127 and high to bot 164
-bot 110 gives low to bot 206 and high to bot 60
-bot 60 gives low to bot 200 and high to bot 141
-bot 134 gives low to bot 67 and high to bot 7
-bot 90 gives low to bot 12 and high to bot 192
-bot 208 gives low to bot 155 and high to bot 182
-bot 87 gives low to bot 28 and high to bot 195
-bot 108 gives low to bot 53 and high to bot 186
-bot 150 gives low to bot 154 and high to bot 56
-bot 204 gives low to output 17 and high to bot 58
-bot 174 gives low to bot 138 and high to bot 67
-bot 195 gives low to bot 147 and high to bot 81
-bot 24 gives low to bot 146 and high to bot 3
-bot 12 gives low to bot 119 and high to bot 9
-value 37 goes to bot 35
-bot 137 gives low to bot 151 and high to bot 170
-bot 1 gives low to output 2 and high to bot 22
-bot 63 gives low to bot 150 and high to bot 8
-bot 133 gives low to bot 140 and high to bot 124
-bot 154 gives low to bot 91 and high to bot 110
-bot 145 gives low to bot 47 and high to bot 18
-bot 109 gives low to bot 159 and high to bot 82
-bot 202 gives low to bot 116 and high to bot 37
-bot 168 gives low to bot 133 and high to bot 177
-bot 193 gives low to bot 93 and high to bot 69
-bot 191 gives low to output 16 and high to bot 21
-bot 135 gives low to bot 82 and high to bot 163
-bot 130 gives low to bot 102 and high to bot 114
-bot 26 gives low to bot 208 and high to bot 159
-bot 152 gives low to bot 22 and high to bot 31
-bot 118 gives low to bot 136 and high to bot 144
-bot 149 gives low to bot 17 and high to bot 54
-bot 64 gives low to bot 164 and high to bot 119
-bot 120 gives low to bot 64 and high to bot 12
-bot 180 gives low to bot 188 and high to bot 130
-bot 203 gives low to bot 204 and high to bot 125
-bot 3 gives low to bot 46 and high to bot 104
-bot 114 gives low to bot 205 and high to bot 79
-bot 25 gives low to bot 194 and high to bot 20
-bot 65 gives low to bot 181 and high to bot 118
-bot 169 gives low to bot 192 and high to bot 117
-bot 51 gives low to output 8 and high to bot 50
-bot 41 gives low to bot 50 and high to bot 145
-bot 20 gives low to bot 23 and high to bot 10
-bot 106 gives low to bot 96 and high to bot 126
-bot 23 gives low to bot 5 and high to bot 6
-value 11 goes to bot 43
-value 47 goes to bot 189
-value 5 goes to bot 115
-bot 46 gives low to bot 51 and high to bot 41
-bot 115 gives low to bot 43 and high to bot 203
-bot 209 gives low to bot 73 and high to bot 187
-bot 16 gives low to bot 113 and high to bot 62
-bot 101 gives low to bot 174 and high to bot 134
-bot 167 gives low to output 20 and high to bot 158
-value 3 goes to bot 133
-bot 184 gives low to bot 125 and high to bot 100
-bot 155 gives low to bot 166 and high to bot 70
-bot 88 gives low to bot 81 and high to bot 84
-value 19 goes to bot 0
-bot 171 gives low to bot 36 and high to bot 45
-bot 186 gives low to bot 199 and high to bot 97
-bot 111 gives low to bot 209 and high to bot 85
-bot 22 gives low to output 4 and high to bot 131
-bot 166 gives low to bot 132 and high to bot 65
-bot 6 gives low to bot 173 and high to bot 52
-bot 75 gives low to bot 104 and high to bot 29
-bot 91 gives low to bot 62 and high to bot 206
-bot 164 gives low to bot 142 and high to bot 38
-bot 15 gives low to bot 160 and high to bot 197
-bot 66 gives low to bot 198 and high to bot 188
-bot 199 gives low to bot 184 and high to bot 33
-bot 122 gives low to bot 55 and high to bot 5
-bot 68 gives low to bot 40 and high to bot 143
-bot 128 gives low to bot 4 and high to bot 94
-bot 27 gives low to bot 13 and high to bot 78
-bot 34 gives low to bot 195 and high to bot 88
-bot 94 gives low to bot 109 and high to bot 135
-bot 158 gives low to output 3 and high to bot 138
-bot 47 gives low to output 15 and high to bot 59
-bot 163 gives low to bot 120 and high to bot 90
-bot 48 gives low to bot 111 and high to bot 102
-bot 40 gives low to bot 207 and high to bot 176
-bot 144 gives low to bot 153 and high to bot 39
-bot 201 gives low to bot 162 and high to bot 83
-bot 72 gives low to bot 115 and high to bot 121
-bot 156 gives low to bot 19 and high to bot 101
-bot 185 gives low to bot 145 and high to bot 183
-bot 103 gives low to bot 8 and high to bot 111
-bot 192 gives low to bot 9 and high to bot 66
-value 71 goes to bot 140
-bot 205 gives low to bot 68 and high to bot 79
-bot 151 gives low to output 11 and high to bot 95
-bot 153 gives low to bot 97 and high to bot 44
-bot 105 gives low to bot 15 and high to bot 175
-bot 11 gives low to bot 183 and high to bot 86
-bot 160 gives low to bot 11 and high to bot 71
-bot 56 gives low to bot 110 and high to bot 73
-bot 207 gives low to bot 172 and high to bot 89
-bot 181 gives low to bot 108 and high to bot 136
-bot 175 gives low to bot 197 and high to bot 106
-bot 69 gives low to bot 167 and high to bot 19
-bot 58 gives low to output 9 and high to bot 1
-bot 78 gives low to bot 74 and high to bot 15
-bot 21 gives low to output 12 and high to output 19
-bot 190 gives low to bot 168 and high to bot 177
-value 29 goes to bot 190
-bot 107 gives low to bot 39 and high to bot 150
-bot 61 gives low to bot 63 and high to bot 103
-bot 52 gives low to bot 202 and high to bot 37
-value 53 goes to bot 168
-bot 30 gives low to bot 3 and high to bot 75
-bot 116 gives low to bot 123 and high to bot 42
-bot 85 gives low to bot 187 and high to bot 205
-bot 99 gives low to bot 94 and high to bot 162
-bot 126 gives low to bot 54 and high to bot 148
-bot 19 gives low to bot 158 and high to bot 174
-bot 82 gives low to bot 49 and high to bot 120
-bot 42 gives low to bot 169 and high to bot 139
-value 41 goes to bot 190
-bot 188 gives low to bot 48 and high to bot 130
-bot 113 gives low to bot 14 and high to bot 157
-bot 177 gives low to bot 124 and high to bot 80
-bot 18 gives low to bot 59 and high to bot 193
-bot 96 gives low to bot 149 and high to bot 126
-bot 62 gives low to bot 157 and high to bot 2
-bot 45 gives low to bot 105 and high to bot 175
-bot 2 gives low to bot 87 and high to bot 34
-bot 147 gives low to bot 170 and high to bot 24
-bot 70 gives low to bot 65 and high to bot 127
-bot 162 gives low to bot 135 and high to bot 165
-bot 117 gives low to bot 66 and high to bot 180
-bot 100 gives low to bot 57 and high to bot 14
-bot 57 gives low to bot 1 and high to bot 152
-bot 121 gives low to bot 203 and high to bot 184
-bot 10 gives low to bot 6 and high to bot 52
-bot 84 gives low to bot 30 and high to bot 13
-value 7 goes to bot 166
-bot 136 gives low to bot 186 and high to bot 153
-bot 161 gives low to bot 32 and high to bot 108
-bot 102 gives low to bot 85 and high to bot 114
-bot 80 gives low to bot 20 and high to bot 10
-bot 200 gives low to bot 34 and high to bot 178
-bot 119 gives low to bot 38 and high to bot 61
-bot 28 gives low to bot 137 and high to bot 147
-bot 35 gives low to bot 128 and high to bot 99
-value 67 goes to bot 132
-bot 146 gives low to bot 112 and high to bot 46
-bot 194 gives low to bot 122 and high to bot 23
-value 73 goes to bot 26
-bot 183 gives low to bot 18 and high to bot 98

data/advent2016/input12.txt

@@ -1,23 +0,0 @@
-cpy 1 a
-cpy 1 b
-cpy 26 d
-jnz c 2
-jnz 1 5
-cpy 7 c
-inc d
-dec c
-jnz c -2
-cpy a c
-inc a
-dec b
-jnz b -2
-cpy c b
-dec d
-jnz d -6
-cpy 14 c
-cpy 14 d
-inc a
-dec d
-jnz d -2
-dec c
-jnz c -5

data/advent2016/input2.txt

@@ -1,5 +0,0 @@
-LURLDDLDULRURDUDLRULRDLLRURDUDRLLRLRURDRULDLRLRRDDULUDULURULLURLURRRLLDURURLLUURDLLDUUDRRDLDLLRUUDURURRULURUURLDLLLUDDUUDRULLRUDURRLRLLDRRUDULLDUUUDLDLRLLRLULDLRLUDLRRULDDDURLUULRDLRULRDURDURUUUDDRRDRRUDULDUUULLLLURRDDUULDRDRLULRRRUUDUURDULDDRLDRDLLDDLRDLDULUDDLULUDRLULRRRRUUUDULULDLUDUUUUDURLUDRDLLDDRULUURDRRRDRLDLLURLULDULRUDRDDUDDLRLRRDUDDRULRULULRDDDDRDLLLRURDDDDRDRUDUDUUDRUDLDULRUULLRRLURRRRUUDRDLDUDDLUDRRURLRDDLUUDUDUUDRLUURURRURDRRRURULUUDUUDURUUURDDDURUDLRLLULRULRDURLLDDULLDULULDDDRUDDDUUDDUDDRRRURRUURRRRURUDRRDLRDUUULLRRRUDD
-DLDUDULDLRDLUDDLLRLUUULLDURRUDLLDUDDRDRLRDDUUUURDULDULLRDRURDLULRUURRDLULUDRURDULLDRURUULLDLLUDRLUDRUDRURURUULRDLLDDDLRUDUDLUDURLDDLRRUUURDDDRLUDDDUDDLDUDDUUUUUULLRDRRUDRUDDDLLLDRDUULRLDURLLDURUDDLLURDDLULLDDDRLUDRDDLDLDLRLURRDURRRUDRRDUUDDRLLUDLDRLRDUDLDLRDRUDUUULULUDRRULUDRDRRLLDDRDDDLULURUURULLRRRRRDDRDDRRRDLRDURURRRDDULLUULRULURURDRRUDURDDUURDUURUURUULURUUDULURRDLRRUUDRLLDLDRRRULDRLLRLDUDULRRLDUDDUUURDUDLDDDUDL
-RURDRUDUUUUULLLUULDULLLDRUULURLDULULRDDLRLLRURULLLLLLRULLURRDLULLUULRRDURRURLUDLULDLRRULRDLDULLDDRRDLLRURRDULULDRRDDULDURRRUUURUDDURULUUDURUULUDLUURRLDLRDDUUUUURULDRDUDDULULRDRUUURRRDRLURRLUUULRUDRRLUDRDLDUDDRDRRUULLLLDUUUULDULRRRLLRLRLRULDLRURRLRLDLRRDRDRLDRUDDDUUDRLLUUURLRLULURLDRRULRULUDRUUURRUDLDDRRDDURUUULLDDLLDDRUDDDUULUDRDDLULDDDDRULDDDDUUUURRLDUURULRDDRDLLLRRDDURUDRRLDUDULRULDDLDDLDUUUULDLLULUUDDULUUDLRDRUDLURDULUDDRDRDRDDURDLURLULRUURDUDULDDLDDRUULLRDRLRRUURRDDRDUDDLRRLLDRDLUUDRRDDDUUUDLRRLDDDUDRURRDDUULUDLLLRUDDRULRLLLRDLUDUUUUURLRRUDUDDDDLRLLULLUDRDURDDULULRDRDLUDDRLURRLRRULRL
-LDUURLLULRUURRDLDRUULRDRDDDRULDLURDDRURULLRUURRLRRLDRURRDRLUDRUUUULLDRLURDRLRUDDRDDDUURRDRRURULLLDRDRDLDUURLDRUULLDRDDRRDRDUUDLURUDDLLUUDDULDDULRDDUUDDDLRLLLULLDLUDRRLDUUDRUUDUDUURULDRRLRRDLRLURDRURURRDURDURRUDLRURURUUDURURUDRURULLLLLUDRUDUDULRLLLRDRLLRLRLRRDULRUUULURLRRLDRRRDRULRUDUURRRRULDDLRULDRRRDLDRLUDLLUDDRURLURURRLRUDLRLLRDLLDRDDLDUDRDLDDRULDDULUDDLLDURDULLDURRURRULLDRLUURURLLUDDRLRRUUDULRRLLRUDRDUURLDDLLURRDLRUURLLDRDLRUULUDURRDULUULDDLUUUDDLRRDRDUDLRUULDDDLDDRUDDD
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

data/advent2016/input21.txt

@@ -1,100 +0,0 @@
-rotate right 3 steps
-swap position 7 with position 0
-rotate left 3 steps
-reverse positions 2 through 5
-move position 6 to position 3
-reverse positions 0 through 4
-swap position 4 with position 2
-rotate based on position of letter d
-rotate right 0 steps
-move position 7 to position 5
-swap position 4 with position 5
-swap position 3 with position 5
-move position 5 to position 3
-swap letter e with letter f
-swap position 6 with position 3
-swap letter a with letter e
-reverse positions 0 through 1
-reverse positions 0 through 4
-swap letter c with letter e
-reverse positions 1 through 7
-rotate right 1 step
-reverse positions 6 through 7
-move position 7 to position 1
-move position 4 to position 0
-move position 4 to position 6
-move position 6 to position 3
-swap position 1 with position 6
-swap position 5 with position 7
-swap position 2 with position 5
-swap position 6 with position 5
-swap position 2 with position 4
-reverse positions 2 through 6
-reverse positions 3 through 5
-move position 3 to position 5
-reverse positions 1 through 5
-rotate left 1 step
-move position 4 to position 5
-swap letter c with letter b
-swap position 2 with position 1
-reverse positions 3 through 4
-swap position 3 with position 4
-reverse positions 5 through 7
-swap letter b with letter d
-reverse positions 3 through 4
-swap letter c with letter h
-rotate based on position of letter b
-rotate based on position of letter e
-rotate right 3 steps
-rotate right 7 steps
-rotate left 2 steps
-move position 6 to position 1
-reverse positions 1 through 3
-rotate based on position of letter b
-reverse positions 0 through 4
-swap letter g with letter c
-move position 1 to position 5
-rotate right 4 steps
-rotate left 2 steps
-move position 7 to position 2
-rotate based on position of letter c
-move position 6 to position 1
-swap letter f with letter g
-rotate right 6 steps
-swap position 6 with position 2
-reverse positions 2 through 6
-swap position 3 with position 1
-rotate based on position of letter h
-reverse positions 2 through 5
-move position 1 to position 3
-rotate right 1 step
-rotate right 7 steps
-move position 6 to position 3
-rotate based on position of letter h
-swap letter d with letter h
-rotate left 0 steps
-move position 1 to position 2
-swap letter a with letter g
-swap letter a with letter g
-swap position 4 with position 2
-rotate right 1 step
-rotate based on position of letter b
-swap position 7 with position 1
-rotate based on position of letter e
-move position 1 to position 4
-move position 6 to position 3
-rotate left 3 steps
-swap letter f with letter g
-swap position 3 with position 1
-swap position 4 with position 3
-swap letter f with letter c
-rotate left 3 steps
-rotate left 0 steps
-rotate right 3 steps
-swap letter d with letter e
-swap position 2 with position 7
-move position 3 to position 6
-swap position 7 with position 1
-swap position 3 with position 6
-rotate left 5 steps
-swap position 2 with position 6

data/advent2016/input22.txt

@@ -1,914 +0,0 @@
-root@ebhq-gridcenter# df -h
-Filesystem              Size  Used  Avail  Use%
-/dev/grid/node-x0-y0     92T   70T    22T   76%
-/dev/grid/node-x0-y1     86T   65T    21T   75%
-/dev/grid/node-x0-y2     88T   73T    15T   82%
-/dev/grid/node-x0-y3     91T   67T    24T   73%
-/dev/grid/node-x0-y4     87T   70T    17T   80%
-/dev/grid/node-x0-y5     91T   70T    21T   76%
-/dev/grid/node-x0-y6     87T   71T    16T   81%
-/dev/grid/node-x0-y7     94T   69T    25T   73%
-/dev/grid/node-x0-y8     93T   69T    24T   74%
-/dev/grid/node-x0-y9     87T   71T    16T   81%
-/dev/grid/node-x0-y10    89T   66T    23T   74%
-/dev/grid/node-x0-y11    92T   64T    28T   69%
-/dev/grid/node-x0-y12    88T   66T    22T   75%
-/dev/grid/node-x0-y13    85T   72T    13T   84%
-/dev/grid/node-x0-y14    94T   68T    26T   72%
-/dev/grid/node-x0-y15    92T   67T    25T   72%
-/dev/grid/node-x0-y16    93T   65T    28T   69%
-/dev/grid/node-x0-y17    91T   67T    24T   73%
-/dev/grid/node-x0-y18    92T   68T    24T   73%
-/dev/grid/node-x0-y19    91T   69T    22T   75%
-/dev/grid/node-x0-y20    89T   65T    24T   73%
-/dev/grid/node-x0-y21    90T   72T    18T   80%
-/dev/grid/node-x0-y22    94T   67T    27T   71%
-/dev/grid/node-x0-y23    86T   72T    14T   83%
-/dev/grid/node-x1-y0     85T   66T    19T   77%
-/dev/grid/node-x1-y1     89T   64T    25T   71%
-/dev/grid/node-x1-y2     92T   67T    25T   72%
-/dev/grid/node-x1-y3     87T   70T    17T   80%
-/dev/grid/node-x1-y4     86T   71T    15T   82%
-/dev/grid/node-x1-y5     91T   68T    23T   74%
-/dev/grid/node-x1-y6     87T   71T    16T   81%
-/dev/grid/node-x1-y7     94T   69T    25T   73%
-/dev/grid/node-x1-y8     89T   70T    19T   78%
-/dev/grid/node-x1-y9     93T   64T    29T   68%
-/dev/grid/node-x1-y10    92T   67T    25T   72%
-/dev/grid/node-x1-y11    92T   72T    20T   78%
-/dev/grid/node-x1-y12    87T   65T    22T   74%
-/dev/grid/node-x1-y13    85T   73T    12T   85%
-/dev/grid/node-x1-y14    89T   70T    19T   78%
-/dev/grid/node-x1-y15    90T   67T    23T   74%
-/dev/grid/node-x1-y16    94T   71T    23T   75%
-/dev/grid/node-x1-y17    93T   68T    25T   73%
-/dev/grid/node-x1-y18    88T   72T    16T   81%
-/dev/grid/node-x1-y19    89T   66T    23T   74%
-/dev/grid/node-x1-y20    88T   70T    18T   79%
-/dev/grid/node-x1-y21    90T   67T    23T   74%
-/dev/grid/node-x1-y22    90T   64T    26T   71%
-/dev/grid/node-x1-y23    92T   69T    23T   75%
-/dev/grid/node-x2-y0     86T   67T    19T   77%
-/dev/grid/node-x2-y1     85T   71T    14T   83%
-/dev/grid/node-x2-y2     91T   69T    22T   75%
-/dev/grid/node-x2-y3     88T   68T    20T   77%
-/dev/grid/node-x2-y4     87T   73T    14T   83%
-/dev/grid/node-x2-y5     94T   64T    30T   68%
-/dev/grid/node-x2-y6     90T   66T    24T   73%
-/dev/grid/node-x2-y7     91T   66T    25T   72%
-/dev/grid/node-x2-y8     86T   64T    22T   74%
-/dev/grid/node-x2-y9     90T   69T    21T   76%
-/dev/grid/node-x2-y10    94T   65T    29T   69%
-/dev/grid/node-x2-y11    89T   69T    20T   77%
-/dev/grid/node-x2-y12    94T   64T    30T   68%
-/dev/grid/node-x2-y13    85T   70T    15T   82%
-/dev/grid/node-x2-y14    87T   69T    18T   79%
-/dev/grid/node-x2-y15    94T   70T    24T   74%
-/dev/grid/node-x2-y16    89T   72T    17T   80%
-/dev/grid/node-x2-y17    94T   65T    29T   69%
-/dev/grid/node-x2-y18    85T   70T    15T   82%
-/dev/grid/node-x2-y19    86T   64T    22T   74%
-/dev/grid/node-x2-y20    91T   69T    22T   75%
-/dev/grid/node-x2-y21    92T   66T    26T   71%
-/dev/grid/node-x2-y22    92T   66T    26T   71%
-/dev/grid/node-x2-y23    94T   70T    24T   74%
-/dev/grid/node-x3-y0     91T   65T    26T   71%
-/dev/grid/node-x3-y1     91T   73T    18T   80%
-/dev/grid/node-x3-y2     93T   67T    26T   72%
-/dev/grid/node-x3-y3     91T   66T    25T   72%
-/dev/grid/node-x3-y4     85T   69T    16T   81%
-/dev/grid/node-x3-y5     94T   69T    25T   73%
-/dev/grid/node-x3-y6     94T   70T    24T   74%
-/dev/grid/node-x3-y7     92T   72T    20T   78%
-/dev/grid/node-x3-y8     94T   73T    21T   77%
-/dev/grid/node-x3-y9     86T   73T    13T   84%
-/dev/grid/node-x3-y10    86T   68T    18T   79%
-/dev/grid/node-x3-y11    87T   65T    22T   74%
-/dev/grid/node-x3-y12    91T   70T    21T   76%
-/dev/grid/node-x3-y13    93T   66T    27T   70%
-/dev/grid/node-x3-y14    92T   71T    21T   77%
-/dev/grid/node-x3-y15    90T   71T    19T   78%
-/dev/grid/node-x3-y16    90T   70T    20T   77%
-/dev/grid/node-x3-y17    94T   66T    28T   70%
-/dev/grid/node-x3-y18    90T   69T    21T   76%
-/dev/grid/node-x3-y19    89T   65T    24T   73%
-/dev/grid/node-x3-y20    90T   72T    18T   80%
-/dev/grid/node-x3-y21    94T   72T    22T   76%
-/dev/grid/node-x3-y22    89T   73T    16T   82%
-/dev/grid/node-x3-y23    85T   69T    16T   81%
-/dev/grid/node-x4-y0     94T   68T    26T   72%
-/dev/grid/node-x4-y1     90T   66T    24T   73%
-/dev/grid/node-x4-y2     89T   70T    19T   78%
-/dev/grid/node-x4-y3     89T   64T    25T   71%
-/dev/grid/node-x4-y4     89T   69T    20T   77%
-/dev/grid/node-x4-y5     85T   64T    21T   75%
-/dev/grid/node-x4-y6     90T   72T    18T   80%
-/dev/grid/node-x4-y7     90T   69T    21T   76%
-/dev/grid/node-x4-y8     89T   70T    19T   78%
-/dev/grid/node-x4-y9     92T   70T    22T   76%
-/dev/grid/node-x4-y10    90T   66T    24T   73%
-/dev/grid/node-x4-y11    85T   71T    14T   83%
-/dev/grid/node-x4-y12    89T   65T    24T   73%
-/dev/grid/node-x4-y13    86T   72T    14T   83%
-/dev/grid/node-x4-y14    91T   72T    19T   79%
-/dev/grid/node-x4-y15    89T   71T    18T   79%
-/dev/grid/node-x4-y16    86T   73T    13T   84%
-/dev/grid/node-x4-y17    91T   65T    26T   71%
-/dev/grid/node-x4-y18    87T   67T    20T   77%
-/dev/grid/node-x4-y19    94T   66T    28T   70%
-/dev/grid/node-x4-y20    89T   73T    16T   82%
-/dev/grid/node-x4-y21    85T   73T    12T   85%
-/dev/grid/node-x4-y22    87T   67T    20T   77%
-/dev/grid/node-x4-y23    91T   66T    25T   72%
-/dev/grid/node-x5-y0     90T   71T    19T   78%
-/dev/grid/node-x5-y1     87T   71T    16T   81%
-/dev/grid/node-x5-y2     87T   69T    18T   79%
-/dev/grid/node-x5-y3     85T   64T    21T   75%
-/dev/grid/node-x5-y4     89T   72T    17T   80%
-/dev/grid/node-x5-y5     88T   65T    23T   73%
-/dev/grid/node-x5-y6     91T   66T    25T   72%
-/dev/grid/node-x5-y7     89T   65T    24T   73%
-/dev/grid/node-x5-y8     86T   68T    18T   79%
-/dev/grid/node-x5-y9     93T   68T    25T   73%
-/dev/grid/node-x5-y10    87T   70T    17T   80%
-/dev/grid/node-x5-y11    93T   72T    21T   77%
-/dev/grid/node-x5-y12    94T   67T    27T   71%
-/dev/grid/node-x5-y13    94T   68T    26T   72%
-/dev/grid/node-x5-y14    92T   72T    20T   78%
-/dev/grid/node-x5-y15    85T   67T    18T   78%
-/dev/grid/node-x5-y16    87T   73T    14T   83%
-/dev/grid/node-x5-y17    85T   69T    16T   81%
-/dev/grid/node-x5-y18    89T   65T    24T   73%
-/dev/grid/node-x5-y19    86T   65T    21T   75%
-/dev/grid/node-x5-y20    85T   70T    15T   82%
-/dev/grid/node-x5-y21    86T   73T    13T   84%
-/dev/grid/node-x5-y22    85T   67T    18T   78%
-/dev/grid/node-x5-y23    93T   64T    29T   68%
-/dev/grid/node-x6-y0     90T   72T    18T   80%
-/dev/grid/node-x6-y1     93T   65T    28T   69%
-/dev/grid/node-x6-y2     85T   64T    21T   75%
-/dev/grid/node-x6-y3     88T   64T    24T   72%
-/dev/grid/node-x6-y4     89T   64T    25T   71%
-/dev/grid/node-x6-y5     86T   72T    14T   83%
-/dev/grid/node-x6-y6     88T   72T    16T   81%
-/dev/grid/node-x6-y7     93T   66T    27T   70%
-/dev/grid/node-x6-y8     90T   65T    25T   72%
-/dev/grid/node-x6-y9     93T   69T    24T   74%
-/dev/grid/node-x6-y10    88T   70T    18T   79%
-/dev/grid/node-x6-y11    85T   73T    12T   85%
-/dev/grid/node-x6-y12    92T   73T    19T   79%
-/dev/grid/node-x6-y13    93T   70T    23T   75%
-/dev/grid/node-x6-y14    85T   69T    16T   81%
-/dev/grid/node-x6-y15    86T   67T    19T   77%
-/dev/grid/node-x6-y16    91T   65T    26T   71%
-/dev/grid/node-x6-y17    91T   66T    25T   72%
-/dev/grid/node-x6-y18    91T   65T    26T   71%
-/dev/grid/node-x6-y19    92T   66T    26T   71%
-/dev/grid/node-x6-y20    90T   64T    26T   71%
-/dev/grid/node-x6-y21    86T   70T    16T   81%
-/dev/grid/node-x6-y22    94T   71T    23T   75%
-/dev/grid/node-x6-y23    90T   69T    21T   76%
-/dev/grid/node-x7-y0     91T   71T    20T   78%
-/dev/grid/node-x7-y1     94T   71T    23T   75%
-/dev/grid/node-x7-y2     88T   64T    24T   72%
-/dev/grid/node-x7-y3     93T   73T    20T   78%
-/dev/grid/node-x7-y4     86T   68T    18T   79%
-/dev/grid/node-x7-y5     88T   73T    15T   82%
-/dev/grid/node-x7-y6     92T   66T    26T   71%
-/dev/grid/node-x7-y7     90T   64T    26T   71%
-/dev/grid/node-x7-y8     88T   64T    24T   72%
-/dev/grid/node-x7-y9     88T   70T    18T   79%
-/dev/grid/node-x7-y10    93T   67T    26T   72%
-/dev/grid/node-x7-y11    88T   71T    17T   80%
-/dev/grid/node-x7-y12    89T   71T    18T   79%
-/dev/grid/node-x7-y13    85T   65T    20T   76%
-/dev/grid/node-x7-y14    85T   70T    15T   82%
-/dev/grid/node-x7-y15    87T   72T    15T   82%
-/dev/grid/node-x7-y16    85T   64T    21T   75%
-/dev/grid/node-x7-y17    85T   64T    21T   75%
-/dev/grid/node-x7-y18    88T   64T    24T   72%
-/dev/grid/node-x7-y19    90T   67T    23T   74%
-/dev/grid/node-x7-y20    94T   66T    28T   70%
-/dev/grid/node-x7-y21    87T   67T    20T   77%
-/dev/grid/node-x7-y22    88T   69T    19T   78%
-/dev/grid/node-x7-y23    93T   69T    24T   74%
-/dev/grid/node-x8-y0     85T   72T    13T   84%
-/dev/grid/node-x8-y1     91T   72T    19T   79%
-/dev/grid/node-x8-y2     86T   65T    21T   75%
-/dev/grid/node-x8-y3     85T   69T    16T   81%
-/dev/grid/node-x8-y4     93T   65T    28T   69%
-/dev/grid/node-x8-y5     87T   72T    15T   82%
-/dev/grid/node-x8-y6     93T   68T    25T   73%
-/dev/grid/node-x8-y7     89T   73T    16T   82%
-/dev/grid/node-x8-y8     85T   65T    20T   76%
-/dev/grid/node-x8-y9     85T   73T    12T   85%
-/dev/grid/node-x8-y10    89T   71T    18T   79%
-/dev/grid/node-x8-y11    90T   68T    22T   75%
-/dev/grid/node-x8-y12    85T   65T    20T   76%
-/dev/grid/node-x8-y13    89T   71T    18T   79%
-/dev/grid/node-x8-y14    92T   71T    21T   77%
-/dev/grid/node-x8-y15    85T   73T    12T   85%
-/dev/grid/node-x8-y16    87T   73T    14T   83%
-/dev/grid/node-x8-y17    92T   66T    26T   71%
-/dev/grid/node-x8-y18    87T   69T    18T   79%
-/dev/grid/node-x8-y19    88T   64T    24T   72%
-/dev/grid/node-x8-y20    88T   68T    20T   77%
-/dev/grid/node-x8-y21    92T   66T    26T   71%
-/dev/grid/node-x8-y22    85T   68T    17T   80%
-/dev/grid/node-x8-y23    91T   66T    25T   72%
-/dev/grid/node-x9-y0     90T   69T    21T   76%
-/dev/grid/node-x9-y1     86T   73T    13T   84%
-/dev/grid/node-x9-y2     92T   72T    20T   78%
-/dev/grid/node-x9-y3     87T   68T    19T   78%
-/dev/grid/node-x9-y4     90T   66T    24T   73%
-/dev/grid/node-x9-y5     91T   64T    27T   70%
-/dev/grid/node-x9-y6     91T   68T    23T   74%
-/dev/grid/node-x9-y7     88T   66T    22T   75%
-/dev/grid/node-x9-y8     85T   72T    13T   84%
-/dev/grid/node-x9-y9     87T   68T    19T   78%
-/dev/grid/node-x9-y10    89T   72T    17T   80%
-/dev/grid/node-x9-y11    85T   66T    19T   77%
-/dev/grid/node-x9-y12    87T   73T    14T   83%
-/dev/grid/node-x9-y13    87T   66T    21T   75%
-/dev/grid/node-x9-y14    92T   67T    25T   72%
-/dev/grid/node-x9-y15    90T   67T    23T   74%
-/dev/grid/node-x9-y16    85T   67T    18T   78%
-/dev/grid/node-x9-y17    86T   70T    16T   81%
-/dev/grid/node-x9-y18    86T   73T    13T   84%
-/dev/grid/node-x9-y19    91T   72T    19T   79%
-/dev/grid/node-x9-y20    93T   69T    24T   74%
-/dev/grid/node-x9-y21    92T   72T    20T   78%
-/dev/grid/node-x9-y22    88T   67T    21T   76%
-/dev/grid/node-x9-y23    91T   64T    27T   70%
-/dev/grid/node-x10-y0    89T   65T    24T   73%
-/dev/grid/node-x10-y1    85T   70T    15T   82%
-/dev/grid/node-x10-y2    87T   65T    22T   74%
-/dev/grid/node-x10-y3    86T   73T    13T   84%
-/dev/grid/node-x10-y4    85T   73T    12T   85%
-/dev/grid/node-x10-y5    94T   65T    29T   69%
-/dev/grid/node-x10-y6    91T   71T    20T   78%
-/dev/grid/node-x10-y7    92T   65T    27T   70%
-/dev/grid/node-x10-y8    92T   70T    22T   76%
-/dev/grid/node-x10-y9    93T   66T    27T   70%
-/dev/grid/node-x10-y10   86T   70T    16T   81%
-/dev/grid/node-x10-y11   86T   73T    13T   84%
-/dev/grid/node-x10-y12   93T   71T    22T   76%
-/dev/grid/node-x10-y13   87T   72T    15T   82%
-/dev/grid/node-x10-y14   93T   70T    23T   75%
-/dev/grid/node-x10-y15   92T   66T    26T   71%
-/dev/grid/node-x10-y16   85T   66T    19T   77%
-/dev/grid/node-x10-y17   94T   71T    23T   75%
-/dev/grid/node-x10-y18   88T   72T    16T   81%
-/dev/grid/node-x10-y19   86T   71T    15T   82%
-/dev/grid/node-x10-y20   90T   64T    26T   71%
-/dev/grid/node-x10-y21   93T   72T    21T   77%
-/dev/grid/node-x10-y22   86T   66T    20T   76%
-/dev/grid/node-x10-y23   91T   73T    18T   80%
-/dev/grid/node-x11-y0    91T   69T    22T   75%
-/dev/grid/node-x11-y1    87T   68T    19T   78%
-/dev/grid/node-x11-y2    93T   70T    23T   75%
-/dev/grid/node-x11-y3    88T   65T    23T   73%
-/dev/grid/node-x11-y4    86T   67T    19T   77%
-/dev/grid/node-x11-y5    90T   67T    23T   74%
-/dev/grid/node-x11-y6    94T   70T    24T   74%
-/dev/grid/node-x11-y7    85T   68T    17T   80%
-/dev/grid/node-x11-y8    88T   66T    22T   75%
-/dev/grid/node-x11-y9    92T   67T    25T   72%
-/dev/grid/node-x11-y10   90T   72T    18T   80%
-/dev/grid/node-x11-y11   85T   73T    12T   85%
-/dev/grid/node-x11-y12   88T   73T    15T   82%
-/dev/grid/node-x11-y13   90T   69T    21T   76%
-/dev/grid/node-x11-y14   86T   68T    18T   79%
-/dev/grid/node-x11-y15   87T   71T    16T   81%
-/dev/grid/node-x11-y16   91T   64T    27T   70%
-/dev/grid/node-x11-y17   87T   67T    20T   77%
-/dev/grid/node-x11-y18   88T   70T    18T   79%
-/dev/grid/node-x11-y19   88T   71T    17T   80%
-/dev/grid/node-x11-y20   91T   68T    23T   74%
-/dev/grid/node-x11-y21   86T   71T    15T   82%
-/dev/grid/node-x11-y22   87T   69T    18T   79%
-/dev/grid/node-x11-y23   93T   68T    25T   73%
-/dev/grid/node-x12-y0    90T   67T    23T   74%
-/dev/grid/node-x12-y1    93T   66T    27T   70%
-/dev/grid/node-x12-y2    85T   70T    15T   82%
-/dev/grid/node-x12-y3    91T   64T    27T   70%
-/dev/grid/node-x12-y4    85T   69T    16T   81%
-/dev/grid/node-x12-y5    87T   66T    21T   75%
-/dev/grid/node-x12-y6    86T   67T    19T   77%
-/dev/grid/node-x12-y7    87T   66T    21T   75%
-/dev/grid/node-x12-y8    86T   65T    21T   75%
-/dev/grid/node-x12-y9    92T   66T    26T   71%
-/dev/grid/node-x12-y10   90T   68T    22T   75%
-/dev/grid/node-x12-y11   94T   72T    22T   76%
-/dev/grid/node-x12-y12   88T   66T    22T   75%
-/dev/grid/node-x12-y13   91T   71T    20T   78%
-/dev/grid/node-x12-y14   88T   68T    20T   77%
-/dev/grid/node-x12-y15   94T   68T    26T   72%
-/dev/grid/node-x12-y16   85T   70T    15T   82%
-/dev/grid/node-x12-y17   93T   72T    21T   77%
-/dev/grid/node-x12-y18   94T   64T    30T   68%
-/dev/grid/node-x12-y19   88T   65T    23T   73%
-/dev/grid/node-x12-y20   89T   67T    22T   75%
-/dev/grid/node-x12-y21   89T   65T    24T   73%
-/dev/grid/node-x12-y22   85T   65T    20T   76%
-/dev/grid/node-x12-y23   88T   65T    23T   73%
-/dev/grid/node-x13-y0    90T   72T    18T   80%
-/dev/grid/node-x13-y1    88T   65T    23T   73%
-/dev/grid/node-x13-y2    89T   71T    18T   79%
-/dev/grid/node-x13-y3    90T   66T    24T   73%
-/dev/grid/node-x13-y4    94T   65T    29T   69%
-/dev/grid/node-x13-y5    88T   65T    23T   73%
-/dev/grid/node-x13-y6    86T   72T    14T   83%
-/dev/grid/node-x13-y7    85T   72T    13T   84%
-/dev/grid/node-x13-y8    90T   71T    19T   78%
-/dev/grid/node-x13-y9    89T   67T    22T   75%
-/dev/grid/node-x13-y10   88T   67T    21T   76%
-/dev/grid/node-x13-y11   87T   70T    17T   80%
-/dev/grid/node-x13-y12   90T   68T    22T   75%
-/dev/grid/node-x13-y13   92T   67T    25T   72%
-/dev/grid/node-x13-y14   89T   65T    24T   73%
-/dev/grid/node-x13-y15   87T   70T    17T   80%
-/dev/grid/node-x13-y16   93T   65T    28T   69%
-/dev/grid/node-x13-y17   88T   64T    24T   72%
-/dev/grid/node-x13-y18   86T   67T    19T   77%
-/dev/grid/node-x13-y19   90T   70T    20T   77%
-/dev/grid/node-x13-y20   92T   67T    25T   72%
-/dev/grid/node-x13-y21   90T   71T    19T   78%
-/dev/grid/node-x13-y22   86T   71T    15T   82%
-/dev/grid/node-x13-y23   87T   69T    18T   79%
-/dev/grid/node-x14-y0    94T   64T    30T   68%
-/dev/grid/node-x14-y1    88T   68T    20T   77%
-/dev/grid/node-x14-y2    91T   70T    21T   76%
-/dev/grid/node-x14-y3    87T   69T    18T   79%
-/dev/grid/node-x14-y4    92T   65T    27T   70%
-/dev/grid/node-x14-y5    90T   67T    23T   74%
-/dev/grid/node-x14-y6    89T   65T    24T   73%
-/dev/grid/node-x14-y7    92T   73T    19T   79%
-/dev/grid/node-x14-y8    86T   66T    20T   76%
-/dev/grid/node-x14-y9    93T   68T    25T   73%
-/dev/grid/node-x14-y10   88T   70T    18T   79%
-/dev/grid/node-x14-y11   93T   67T    26T   72%
-/dev/grid/node-x14-y12   85T   70T    15T   82%
-/dev/grid/node-x14-y13   88T   64T    24T   72%
-/dev/grid/node-x14-y14   88T   70T    18T   79%
-/dev/grid/node-x14-y15   90T   70T    20T   77%
-/dev/grid/node-x14-y16   91T   65T    26T   71%
-/dev/grid/node-x14-y17   89T   64T    25T   71%
-/dev/grid/node-x14-y18   85T   73T    12T   85%
-/dev/grid/node-x14-y19   94T   64T    30T   68%
-/dev/grid/node-x14-y20   89T   73T    16T   82%
-/dev/grid/node-x14-y21   91T   73T    18T   80%
-/dev/grid/node-x14-y22   94T   72T    22T   76%
-/dev/grid/node-x14-y23   90T   68T    22T   75%
-/dev/grid/node-x15-y0    91T   71T    20T   78%
-/dev/grid/node-x15-y1    90T   68T    22T   75%
-/dev/grid/node-x15-y2    90T   65T    25T   72%
-/dev/grid/node-x15-y3    90T   68T    22T   75%
-/dev/grid/node-x15-y4    90T   73T    17T   81%
-/dev/grid/node-x15-y5    88T   73T    15T   82%
-/dev/grid/node-x15-y6    88T   66T    22T   75%
-/dev/grid/node-x15-y7    94T   69T    25T   73%
-/dev/grid/node-x15-y8    94T   64T    30T   68%
-/dev/grid/node-x15-y9    93T   65T    28T   69%
-/dev/grid/node-x15-y10   94T   72T    22T   76%
-/dev/grid/node-x15-y11   85T   71T    14T   83%
-/dev/grid/node-x15-y12   93T   67T    26T   72%
-/dev/grid/node-x15-y13   85T   69T    16T   81%
-/dev/grid/node-x15-y14   85T   64T    21T   75%
-/dev/grid/node-x15-y15   88T   65T    23T   73%
-/dev/grid/node-x15-y16   93T   69T    24T   74%
-/dev/grid/node-x15-y17   85T   64T    21T   75%
-/dev/grid/node-x15-y18   89T   72T    17T   80%
-/dev/grid/node-x15-y19   89T   66T    23T   74%
-/dev/grid/node-x15-y20   91T   66T    25T   72%
-/dev/grid/node-x15-y21   90T   71T    19T   78%
-/dev/grid/node-x15-y22   94T   66T    28T   70%
-/dev/grid/node-x15-y23   91T   69T    22T   75%
-/dev/grid/node-x16-y0    94T   64T    30T   68%
-/dev/grid/node-x16-y1    89T   73T    16T   82%
-/dev/grid/node-x16-y2    91T   69T    22T   75%
-/dev/grid/node-x16-y3    94T   71T    23T   75%
-/dev/grid/node-x16-y4    88T   70T    18T   79%
-/dev/grid/node-x16-y5    92T   69T    23T   75%
-/dev/grid/node-x16-y6    93T   67T    26T   72%
-/dev/grid/node-x16-y7    90T   65T    25T   72%
-/dev/grid/node-x16-y8    86T   69T    17T   80%
-/dev/grid/node-x16-y9    87T   71T    16T   81%
-/dev/grid/node-x16-y10   86T   65T    21T   75%
-/dev/grid/node-x16-y11   86T   65T    21T   75%
-/dev/grid/node-x16-y12   85T   73T    12T   85%
-/dev/grid/node-x16-y13   88T   68T    20T   77%
-/dev/grid/node-x16-y14   88T   66T    22T   75%
-/dev/grid/node-x16-y15   93T   66T    27T   70%
-/dev/grid/node-x16-y16   93T   64T    29T   68%
-/dev/grid/node-x16-y17   89T   72T    17T   80%
-/dev/grid/node-x16-y18   91T   65T    26T   71%
-/dev/grid/node-x16-y19   93T   67T    26T   72%
-/dev/grid/node-x16-y20   90T   69T    21T   76%
-/dev/grid/node-x16-y21   87T   68T    19T   78%
-/dev/grid/node-x16-y22   89T   71T    18T   79%
-/dev/grid/node-x16-y23   91T   67T    24T   73%
-/dev/grid/node-x17-y0    87T   64T    23T   73%
-/dev/grid/node-x17-y1    85T   69T    16T   81%
-/dev/grid/node-x17-y2    94T   72T    22T   76%
-/dev/grid/node-x17-y3    87T   67T    20T   77%
-/dev/grid/node-x17-y4    88T   69T    19T   78%
-/dev/grid/node-x17-y5    87T   71T    16T   81%
-/dev/grid/node-x17-y6    87T   70T    17T   80%
-/dev/grid/node-x17-y7    86T   73T    13T   84%
-/dev/grid/node-x17-y8    92T   64T    28T   69%
-/dev/grid/node-x17-y9    85T   64T    21T   75%
-/dev/grid/node-x17-y10   89T   65T    24T   73%
-/dev/grid/node-x17-y11   93T   69T    24T   74%
-/dev/grid/node-x17-y12   85T   67T    18T   78%
-/dev/grid/node-x17-y13   94T   66T    28T   70%
-/dev/grid/node-x17-y14   87T   70T    17T   80%
-/dev/grid/node-x17-y15   88T   73T    15T   82%
-/dev/grid/node-x17-y16   90T   68T    22T   75%
-/dev/grid/node-x17-y17   86T   71T    15T   82%
-/dev/grid/node-x17-y18   91T   72T    19T   79%
-/dev/grid/node-x17-y19   92T   71T    21T   77%
-/dev/grid/node-x17-y20   92T   68T    24T   73%
-/dev/grid/node-x17-y21   89T   67T    22T   75%
-/dev/grid/node-x17-y22   89T   67T    22T   75%
-/dev/grid/node-x17-y23   93T   65T    28T   69%
-/dev/grid/node-x18-y0    87T   70T    17T   80%
-/dev/grid/node-x18-y1    85T   65T    20T   76%
-/dev/grid/node-x18-y2    93T   67T    26T   72%
-/dev/grid/node-x18-y3    92T   65T    27T   70%
-/dev/grid/node-x18-y4    87T   72T    15T   82%
-/dev/grid/node-x18-y5    94T   65T    29T   69%
-/dev/grid/node-x18-y6    92T   67T    25T   72%
-/dev/grid/node-x18-y7    90T   65T    25T   72%
-/dev/grid/node-x18-y8    88T   65T    23T   73%
-/dev/grid/node-x18-y9    87T   70T    17T   80%
-/dev/grid/node-x18-y10   88T   64T    24T   72%
-/dev/grid/node-x18-y11   87T   65T    22T   74%
-/dev/grid/node-x18-y12   88T   66T    22T   75%
-/dev/grid/node-x18-y13   93T   72T    21T   77%
-/dev/grid/node-x18-y14   90T   65T    25T   72%
-/dev/grid/node-x18-y15   89T   66T    23T   74%
-/dev/grid/node-x18-y16   86T   65T    21T   75%
-/dev/grid/node-x18-y17   85T   66T    19T   77%
-/dev/grid/node-x18-y18   91T   69T    22T   75%
-/dev/grid/node-x18-y19   88T   64T    24T   72%
-/dev/grid/node-x18-y20   87T   66T    21T   75%
-/dev/grid/node-x18-y21   87T   69T    18T   79%
-/dev/grid/node-x18-y22   89T   69T    20T   77%
-/dev/grid/node-x18-y23   87T   71T    16T   81%
-/dev/grid/node-x19-y0    89T   72T    17T   80%
-/dev/grid/node-x19-y1    91T   70T    21T   76%
-/dev/grid/node-x19-y2    87T   64T    23T   73%
-/dev/grid/node-x19-y3    88T   70T    18T   79%
-/dev/grid/node-x19-y4    91T   64T    27T   70%
-/dev/grid/node-x19-y5    90T   64T    26T   71%
-/dev/grid/node-x19-y6    91T   65T    26T   71%
-/dev/grid/node-x19-y7    89T   73T    16T   82%
-/dev/grid/node-x19-y8    87T   65T    22T   74%
-/dev/grid/node-x19-y9    90T   66T    24T   73%
-/dev/grid/node-x19-y10   93T   68T    25T   73%
-/dev/grid/node-x19-y11   87T   69T    18T   79%
-/dev/grid/node-x19-y12   92T   66T    26T   71%
-/dev/grid/node-x19-y13   94T   71T    23T   75%
-/dev/grid/node-x19-y14   86T   64T    22T   74%
-/dev/grid/node-x19-y15   89T   68T    21T   76%
-/dev/grid/node-x19-y16   94T   69T    25T   73%
-/dev/grid/node-x19-y17   85T   72T    13T   84%
-/dev/grid/node-x19-y18   93T   70T    23T   75%
-/dev/grid/node-x19-y19   85T   67T    18T   78%
-/dev/grid/node-x19-y20   92T   64T    28T   69%
-/dev/grid/node-x19-y21   93T   68T    25T   73%
-/dev/grid/node-x19-y22   94T   66T    28T   70%
-/dev/grid/node-x19-y23   87T   70T    17T   80%
-/dev/grid/node-x20-y0    91T   65T    26T   71%
-/dev/grid/node-x20-y1    85T   72T    13T   84%
-/dev/grid/node-x20-y2    94T   64T    30T   68%
-/dev/grid/node-x20-y3    89T   65T    24T   73%
-/dev/grid/node-x20-y4    88T   69T    19T   78%
-/dev/grid/node-x20-y5    94T   71T    23T   75%
-/dev/grid/node-x20-y6    87T   69T    18T   79%
-/dev/grid/node-x20-y7    94T   67T    27T   71%
-/dev/grid/node-x20-y8    89T   65T    24T   73%
-/dev/grid/node-x20-y9    88T   65T    23T   73%
-/dev/grid/node-x20-y10   94T   73T    21T   77%
-/dev/grid/node-x20-y11   87T   66T    21T   75%
-/dev/grid/node-x20-y12   92T   66T    26T   71%
-/dev/grid/node-x20-y13   86T   71T    15T   82%
-/dev/grid/node-x20-y14   93T   64T    29T   68%
-/dev/grid/node-x20-y15   91T   65T    26T   71%
-/dev/grid/node-x20-y16   89T   65T    24T   73%
-/dev/grid/node-x20-y17   90T   68T    22T   75%
-/dev/grid/node-x20-y18   90T   73T    17T   81%
-/dev/grid/node-x20-y19   85T   73T    12T   85%
-/dev/grid/node-x20-y20   85T   67T    18T   78%
-/dev/grid/node-x20-y21   94T   65T    29T   69%
-/dev/grid/node-x20-y22   86T   69T    17T   80%
-/dev/grid/node-x20-y23   93T   73T    20T   78%
-/dev/grid/node-x21-y0    92T   73T    19T   79%
-/dev/grid/node-x21-y1    94T   72T    22T   76%
-/dev/grid/node-x21-y2    92T   69T    23T   75%
-/dev/grid/node-x21-y3    86T   68T    18T   79%
-/dev/grid/node-x21-y4    87T   69T    18T   79%
-/dev/grid/node-x21-y5    87T   67T    20T   77%
-/dev/grid/node-x21-y6    87T   70T    17T   80%
-/dev/grid/node-x21-y7    87T   73T    14T   83%
-/dev/grid/node-x21-y8    91T   71T    20T   78%
-/dev/grid/node-x21-y9    85T   68T    17T   80%
-/dev/grid/node-x21-y10   85T   70T    15T   82%
-/dev/grid/node-x21-y11   86T   66T    20T   76%
-/dev/grid/node-x21-y12   90T   64T    26T   71%
-/dev/grid/node-x21-y13   87T   69T    18T   79%
-/dev/grid/node-x21-y14   92T   64T    28T   69%
-/dev/grid/node-x21-y15   88T   65T    23T   73%
-/dev/grid/node-x21-y16   93T   70T    23T   75%
-/dev/grid/node-x21-y17   87T   71T    16T   81%
-/dev/grid/node-x21-y18   91T   65T    26T   71%
-/dev/grid/node-x21-y19   85T   68T    17T   80%
-/dev/grid/node-x21-y20   87T   66T    21T   75%
-/dev/grid/node-x21-y21   94T   72T    22T   76%
-/dev/grid/node-x21-y22   92T   67T    25T   72%
-/dev/grid/node-x21-y23   88T   68T    20T   77%
-/dev/grid/node-x22-y0    88T   69T    19T   78%
-/dev/grid/node-x22-y1    88T   70T    18T   79%
-/dev/grid/node-x22-y2    85T   67T    18T   78%
-/dev/grid/node-x22-y3    86T   67T    19T   77%
-/dev/grid/node-x22-y4    93T   70T    23T   75%
-/dev/grid/node-x22-y5    89T   71T    18T   79%
-/dev/grid/node-x22-y6    90T   73T    17T   81%
-/dev/grid/node-x22-y7    87T   70T    17T   80%
-/dev/grid/node-x22-y8    85T   68T    17T   80%
-/dev/grid/node-x22-y9    87T   64T    23T   73%
-/dev/grid/node-x22-y10   85T   72T    13T   84%
-/dev/grid/node-x22-y11   88T   66T    22T   75%
-/dev/grid/node-x22-y12   87T   72T    15T   82%
-/dev/grid/node-x22-y13   88T   72T    16T   81%
-/dev/grid/node-x22-y14   91T   69T    22T   75%
-/dev/grid/node-x22-y15   90T   73T    17T   81%
-/dev/grid/node-x22-y16   91T   69T    22T   75%
-/dev/grid/node-x22-y17   92T   66T    26T   71%
-/dev/grid/node-x22-y18   94T   70T    24T   74%
-/dev/grid/node-x22-y19   86T   67T    19T   77%
-/dev/grid/node-x22-y20   92T   70T    22T   76%
-/dev/grid/node-x22-y21   89T   71T    18T   79%
-/dev/grid/node-x22-y22   92T   69T    23T   75%
-/dev/grid/node-x22-y23   87T   70T    17T   80%
-/dev/grid/node-x23-y0    88T   69T    19T   78%
-/dev/grid/node-x23-y1    86T   72T    14T   83%
-/dev/grid/node-x23-y2    89T   64T    25T   71%
-/dev/grid/node-x23-y3    91T   68T    23T   74%
-/dev/grid/node-x23-y4    87T   71T    16T   81%
-/dev/grid/node-x23-y5    85T   71T    14T   83%
-/dev/grid/node-x23-y6    92T   68T    24T   73%
-/dev/grid/node-x23-y7    85T   71T    14T   83%
-/dev/grid/node-x23-y8    91T   64T    27T   70%
-/dev/grid/node-x23-y9    85T   70T    15T   82%
-/dev/grid/node-x23-y10   93T   72T    21T   77%
-/dev/grid/node-x23-y11   87T   72T    15T   82%
-/dev/grid/node-x23-y12   90T   72T    18T   80%
-/dev/grid/node-x23-y13   89T   64T    25T   71%
-/dev/grid/node-x23-y14   87T   67T    20T   77%
-/dev/grid/node-x23-y15   87T   70T    17T   80%
-/dev/grid/node-x23-y16   94T   68T    26T   72%
-/dev/grid/node-x23-y17   88T   68T    20T   77%
-/dev/grid/node-x23-y18   87T   65T    22T   74%
-/dev/grid/node-x23-y19   90T   71T    19T   78%
-/dev/grid/node-x23-y20   93T   71T    22T   76%
-/dev/grid/node-x23-y21   92T   64T    28T   69%
-/dev/grid/node-x23-y22   89T   66T    23T   74%
-/dev/grid/node-x23-y23   90T   73T    17T   81%
-/dev/grid/node-x24-y0    93T   70T    23T   75%
-/dev/grid/node-x24-y1    91T   71T    20T   78%
-/dev/grid/node-x24-y2    93T   68T    25T   73%
-/dev/grid/node-x24-y3    88T   72T    16T   81%
-/dev/grid/node-x24-y4    92T   64T    28T   69%
-/dev/grid/node-x24-y5    87T   64T    23T   73%
-/dev/grid/node-x24-y6    91T   70T    21T   76%
-/dev/grid/node-x24-y7    93T   72T    21T   77%
-/dev/grid/node-x24-y8    94T   73T    21T   77%
-/dev/grid/node-x24-y9    88T   72T    16T   81%
-/dev/grid/node-x24-y10   89T   67T    22T   75%
-/dev/grid/node-x24-y11   89T   68T    21T   76%
-/dev/grid/node-x24-y12   89T   66T    23T   74%
-/dev/grid/node-x24-y13   93T   67T    26T   72%
-/dev/grid/node-x24-y14   92T   69T    23T   75%
-/dev/grid/node-x24-y15   85T   72T    13T   84%
-/dev/grid/node-x24-y16   85T   64T    21T   75%
-/dev/grid/node-x24-y17   94T   69T    25T   73%
-/dev/grid/node-x24-y18   93T   67T    26T   72%
-/dev/grid/node-x24-y19   89T   67T    22T   75%
-/dev/grid/node-x24-y20   86T   67T    19T   77%
-/dev/grid/node-x24-y21   87T   71T    16T   81%
-/dev/grid/node-x24-y22   90T   71T    19T   78%
-/dev/grid/node-x24-y23   88T   70T    18T   79%
-/dev/grid/node-x25-y0    91T   70T    21T   76%
-/dev/grid/node-x25-y1    92T   67T    25T   72%
-/dev/grid/node-x25-y2    91T   71T    20T   78%
-/dev/grid/node-x25-y3    88T   68T    20T   77%
-/dev/grid/node-x25-y4    91T   64T    27T   70%
-/dev/grid/node-x25-y5    88T   66T    22T   75%
-/dev/grid/node-x25-y6    89T   66T    23T   74%
-/dev/grid/node-x25-y7    92T   72T    20T   78%
-/dev/grid/node-x25-y8    88T   71T    17T   80%
-/dev/grid/node-x25-y9    90T   65T    25T   72%
-/dev/grid/node-x25-y10   93T   65T    28T   69%
-/dev/grid/node-x25-y11   94T   70T    24T   74%
-/dev/grid/node-x25-y12   90T   69T    21T   76%
-/dev/grid/node-x25-y13   86T   66T    20T   76%
-/dev/grid/node-x25-y14   85T   71T    14T   83%
-/dev/grid/node-x25-y15   91T   72T    19T   79%
-/dev/grid/node-x25-y16   86T   68T    18T   79%
-/dev/grid/node-x25-y17   85T   65T    20T   76%
-/dev/grid/node-x25-y18   85T   67T    18T   78%
-/dev/grid/node-x25-y19   94T   72T    22T   76%
-/dev/grid/node-x25-y20   89T   69T    20T   77%
-/dev/grid/node-x25-y21   94T   70T    24T   74%
-/dev/grid/node-x25-y22   89T   68T    21T   76%
-/dev/grid/node-x25-y23   89T   69T    20T   77%
-/dev/grid/node-x26-y0    91T   64T    27T   70%
-/dev/grid/node-x26-y1    85T   64T    21T   75%
-/dev/grid/node-x26-y2    91T   73T    18T   80%
-/dev/grid/node-x26-y3    94T   66T    28T   70%
-/dev/grid/node-x26-y4    94T   67T    27T   71%
-/dev/grid/node-x26-y5    85T   64T    21T   75%
-/dev/grid/node-x26-y6    94T   73T    21T   77%
-/dev/grid/node-x26-y7    92T   71T    21T   77%
-/dev/grid/node-x26-y8    89T   67T    22T   75%
-/dev/grid/node-x26-y9    89T   72T    17T   80%
-/dev/grid/node-x26-y10   92T   73T    19T   79%
-/dev/grid/node-x26-y11   91T   68T    23T   74%
-/dev/grid/node-x26-y12   90T   64T    26T   71%
-/dev/grid/node-x26-y13   86T   66T    20T   76%
-/dev/grid/node-x26-y14   92T   64T    28T   69%
-/dev/grid/node-x26-y15   91T   64T    27T   70%
-/dev/grid/node-x26-y16   93T   69T    24T   74%
-/dev/grid/node-x26-y17   90T   68T    22T   75%
-/dev/grid/node-x26-y18   91T   64T    27T   70%
-/dev/grid/node-x26-y19   85T   73T    12T   85%
-/dev/grid/node-x26-y20   92T   68T    24T   73%
-/dev/grid/node-x26-y21   87T   67T    20T   77%
-/dev/grid/node-x26-y22   93T   72T    21T   77%
-/dev/grid/node-x26-y23   88T   66T    22T   75%
-/dev/grid/node-x27-y0    92T   69T    23T   75%
-/dev/grid/node-x27-y1    85T   64T    21T   75%
-/dev/grid/node-x27-y2    90T   67T    23T   74%
-/dev/grid/node-x27-y3    87T   69T    18T   79%
-/dev/grid/node-x27-y4    86T   68T    18T   79%
-/dev/grid/node-x27-y5    92T   73T    19T   79%
-/dev/grid/node-x27-y6    93T   65T    28T   69%
-/dev/grid/node-x27-y7    89T   64T    25T   71%
-/dev/grid/node-x27-y8    90T   67T    23T   74%
-/dev/grid/node-x27-y9    89T   66T    23T   74%
-/dev/grid/node-x27-y10   89T   72T    17T   80%
-/dev/grid/node-x27-y11   85T   70T    15T   82%
-/dev/grid/node-x27-y12   89T   70T    19T   78%
-/dev/grid/node-x27-y13   92T   65T    27T   70%
-/dev/grid/node-x27-y14   88T   64T    24T   72%
-/dev/grid/node-x27-y15   89T   70T    19T   78%
-/dev/grid/node-x27-y16   85T   72T    13T   84%
-/dev/grid/node-x27-y17   93T   71T    22T   76%
-/dev/grid/node-x27-y18   94T   72T    22T   76%
-/dev/grid/node-x27-y19   90T   69T    21T   76%
-/dev/grid/node-x27-y20   86T   69T    17T   80%
-/dev/grid/node-x27-y21   90T   68T    22T   75%
-/dev/grid/node-x27-y22   85T   70T    15T   82%
-/dev/grid/node-x27-y23   91T   71T    20T   78%
-/dev/grid/node-x28-y0    88T   68T    20T   77%
-/dev/grid/node-x28-y1    92T   67T    25T   72%
-/dev/grid/node-x28-y2    88T   66T    22T   75%
-/dev/grid/node-x28-y3    87T   69T    18T   79%
-/dev/grid/node-x28-y4    88T   66T    22T   75%
-/dev/grid/node-x28-y5    89T   67T    22T   75%
-/dev/grid/node-x28-y6    94T   64T    30T   68%
-/dev/grid/node-x28-y7    92T   64T    28T   69%
-/dev/grid/node-x28-y8    93T   65T    28T   69%
-/dev/grid/node-x28-y9    90T   66T    24T   73%
-/dev/grid/node-x28-y10   93T   67T    26T   72%
-/dev/grid/node-x28-y11   94T   71T    23T   75%
-/dev/grid/node-x28-y12   85T   69T    16T   81%
-/dev/grid/node-x28-y13   86T   73T    13T   84%
-/dev/grid/node-x28-y14   93T   64T    29T   68%
-/dev/grid/node-x28-y15   88T   64T    24T   72%
-/dev/grid/node-x28-y16   86T   65T    21T   75%
-/dev/grid/node-x28-y17   92T   72T    20T   78%
-/dev/grid/node-x28-y18   88T   64T    24T   72%
-/dev/grid/node-x28-y19   85T   72T    13T   84%
-/dev/grid/node-x28-y20   90T   73T    17T   81%
-/dev/grid/node-x28-y21   85T   68T    17T   80%
-/dev/grid/node-x28-y22   91T   69T    22T   75%
-/dev/grid/node-x28-y23   90T   67T    23T   74%
-/dev/grid/node-x29-y0    89T   71T    18T   79%
-/dev/grid/node-x29-y1    89T   67T    22T   75%
-/dev/grid/node-x29-y2    89T   70T    19T   78%
-/dev/grid/node-x29-y3    91T   64T    27T   70%
-/dev/grid/node-x29-y4    91T   70T    21T   76%
-/dev/grid/node-x29-y5    91T   68T    23T   74%
-/dev/grid/node-x29-y6    88T   72T    16T   81%
-/dev/grid/node-x29-y7    88T   65T    23T   73%
-/dev/grid/node-x29-y8    94T   67T    27T   71%
-/dev/grid/node-x29-y9    92T   69T    23T   75%
-/dev/grid/node-x29-y10   92T   70T    22T   76%
-/dev/grid/node-x29-y11   91T   64T    27T   70%
-/dev/grid/node-x29-y12   85T   73T    12T   85%
-/dev/grid/node-x29-y13   87T   68T    19T   78%
-/dev/grid/node-x29-y14   90T   71T    19T   78%
-/dev/grid/node-x29-y15   93T   68T    25T   73%
-/dev/grid/node-x29-y16   89T   69T    20T   77%
-/dev/grid/node-x29-y17   86T   68T    18T   79%
-/dev/grid/node-x29-y18   91T   65T    26T   71%
-/dev/grid/node-x29-y19   86T   67T    19T   77%
-/dev/grid/node-x29-y20   89T   69T    20T   77%
-/dev/grid/node-x29-y21   87T   72T    15T   82%
-/dev/grid/node-x29-y22   93T   71T    22T   76%
-/dev/grid/node-x29-y23   90T   70T    20T   77%
-/dev/grid/node-x30-y0    86T   65T    21T   75%
-/dev/grid/node-x30-y1    86T   68T    18T   79%
-/dev/grid/node-x30-y2    88T   66T    22T   75%
-/dev/grid/node-x30-y3    86T   67T    19T   77%
-/dev/grid/node-x30-y4    90T   73T    17T   81%
-/dev/grid/node-x30-y5    86T   70T    16T   81%
-/dev/grid/node-x30-y6    89T   72T    17T   80%
-/dev/grid/node-x30-y7    85T   73T    12T   85%
-/dev/grid/node-x30-y8    94T   64T    30T   68%
-/dev/grid/node-x30-y9    89T   67T    22T   75%
-/dev/grid/node-x30-y10   85T   68T    17T   80%
-/dev/grid/node-x30-y11   87T   69T    18T   79%
-/dev/grid/node-x30-y12   94T   68T    26T   72%
-/dev/grid/node-x30-y13   86T   67T    19T   77%
-/dev/grid/node-x30-y14   88T   71T    17T   80%
-/dev/grid/node-x30-y15   89T   68T    21T   76%
-/dev/grid/node-x30-y16   86T   70T    16T   81%
-/dev/grid/node-x30-y17   86T   66T    20T   76%
-/dev/grid/node-x30-y18   86T   72T    14T   83%
-/dev/grid/node-x30-y19  501T  493T     8T   98%
-/dev/grid/node-x30-y20   86T   71T    15T   82%
-/dev/grid/node-x30-y21   94T   68T    26T   72%
-/dev/grid/node-x30-y22   88T   73T    15T   82%
-/dev/grid/node-x30-y23   88T   73T    15T   82%
-/dev/grid/node-x31-y0    88T   73T    15T   82%
-/dev/grid/node-x31-y1    86T   70T    16T   81%
-/dev/grid/node-x31-y2    87T   67T    20T   77%
-/dev/grid/node-x31-y3    87T   72T    15T   82%
-/dev/grid/node-x31-y4    89T   72T    17T   80%
-/dev/grid/node-x31-y5    91T   69T    22T   75%
-/dev/grid/node-x31-y6    94T   71T    23T   75%
-/dev/grid/node-x31-y7    87T   72T    15T   82%
-/dev/grid/node-x31-y8    86T   69T    17T   80%
-/dev/grid/node-x31-y9    90T   72T    18T   80%
-/dev/grid/node-x31-y10   86T   64T    22T   74%
-/dev/grid/node-x31-y11   92T   72T    20T   78%
-/dev/grid/node-x31-y12   94T   72T    22T   76%
-/dev/grid/node-x31-y13   90T   71T    19T   78%
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data/advent2016/input24.txt

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data/advent2016/input4.txt

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-zuv-ykixkz-yigbktmkx-natz-zkinturume-410[kzitu]
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data/advent2016/input6.txt

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data/advent2016/input8.txt

@@ -1,194 +0,0 @@
-rect 1x1
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-rect 1x1
-rotate row y=0 by 5
-rect 1x1
-rotate row y=0 by 5
-rect 1x1
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-rect 1x1
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-rotate row y=0 by 2
-rect 1x1
-rotate row y=0 by 3
-rect 2x1
-rotate row y=0 by 7
-rect 6x1
-rotate row y=0 by 3
-rect 2x1
-rotate row y=0 by 2
-rect 1x2
-rotate row y=1 by 10
-rotate row y=0 by 3
-rotate column x=0 by 1
-rect 2x1
-rotate column x=20 by 1
-rotate column x=15 by 1
-rotate column x=5 by 1
-rotate row y=1 by 5
-rotate row y=0 by 2
-rect 1x2
-rotate row y=0 by 5
-rotate column x=0 by 1
-rect 4x1
-rotate row y=2 by 15
-rotate row y=0 by 5
-rotate column x=0 by 1
-rect 4x1
-rotate row y=2 by 5
-rotate row y=0 by 5
-rotate column x=0 by 1
-rect 4x1
-rotate row y=2 by 10
-rotate row y=0 by 10
-rotate column x=8 by 1
-rotate column x=5 by 1
-rotate column x=0 by 1
-rect 9x1
-rotate column x=27 by 1
-rotate row y=0 by 5
-rotate column x=0 by 1
-rect 4x1
-rotate column x=42 by 1
-rotate column x=40 by 1
-rotate column x=22 by 1
-rotate column x=17 by 1
-rotate column x=12 by 1
-rotate column x=7 by 1
-rotate column x=2 by 1
-rotate row y=3 by 10
-rotate row y=2 by 5
-rotate row y=1 by 3
-rotate row y=0 by 10
-rect 1x4
-rotate column x=37 by 2
-rotate row y=3 by 18
-rotate row y=2 by 30
-rotate row y=1 by 7
-rotate row y=0 by 2
-rotate column x=13 by 3
-rotate column x=12 by 1
-rotate column x=10 by 1
-rotate column x=7 by 1
-rotate column x=6 by 3
-rotate column x=5 by 1
-rotate column x=3 by 3
-rotate column x=2 by 1
-rotate column x=0 by 1
-rect 14x1
-rotate column x=38 by 3
-rotate row y=3 by 12
-rotate row y=2 by 10
-rotate row y=0 by 10
-rotate column x=7 by 1
-rotate column x=5 by 1
-rotate column x=2 by 1
-rotate column x=0 by 1
-rect 9x1
-rotate row y=4 by 20
-rotate row y=3 by 25
-rotate row y=2 by 10
-rotate row y=0 by 15
-rotate column x=12 by 1
-rotate column x=10 by 1
-rotate column x=8 by 3
-rotate column x=7 by 1
-rotate column x=5 by 1
-rotate column x=3 by 3
-rotate column x=2 by 1
-rotate column x=0 by 1
-rect 14x1
-rotate column x=34 by 1
-rotate row y=1 by 45
-rotate column x=47 by 1
-rotate column x=42 by 1
-rotate column x=19 by 1
-rotate column x=9 by 2
-rotate row y=4 by 7
-rotate row y=3 by 20
-rotate row y=0 by 7
-rotate column x=5 by 1
-rotate column x=3 by 1
-rotate column x=2 by 1
-rotate column x=0 by 1
-rect 6x1
-rotate row y=4 by 8
-rotate row y=3 by 5
-rotate row y=1 by 5
-rotate column x=5 by 1
-rotate column x=4 by 1
-rotate column x=3 by 2
-rotate column x=2 by 1
-rotate column x=1 by 3
-rotate column x=0 by 1
-rect 6x1
-rotate column x=36 by 3
-rotate column x=25 by 3
-rotate column x=18 by 3
-rotate column x=11 by 3
-rotate column x=3 by 4
-rotate row y=4 by 5
-rotate row y=3 by 5
-rotate row y=2 by 8
-rotate row y=1 by 8
-rotate row y=0 by 3
-rotate column x=3 by 4
-rotate column x=0 by 4
-rect 4x4
-rotate row y=4 by 10
-rotate row y=3 by 20
-rotate row y=1 by 10
-rotate row y=0 by 10
-rotate column x=8 by 1
-rotate column x=7 by 1
-rotate column x=6 by 1
-rotate column x=5 by 1
-rotate column x=3 by 1
-rotate column x=2 by 1
-rotate column x=1 by 1
-rotate column x=0 by 1
-rect 9x1
-rotate row y=0 by 40
-rotate column x=44 by 1
-rotate column x=35 by 5
-rotate column x=18 by 5
-rotate column x=15 by 3
-rotate column x=10 by 5
-rotate row y=5 by 15
-rotate row y=4 by 10
-rotate row y=3 by 40
-rotate row y=2 by 20
-rotate row y=1 by 45
-rotate row y=0 by 35
-rotate column x=48 by 1
-rotate column x=47 by 5
-rotate column x=46 by 5
-rotate column x=45 by 1
-rotate column x=43 by 1
-rotate column x=40 by 1
-rotate column x=38 by 2
-rotate column x=37 by 3
-rotate column x=36 by 2
-rotate column x=32 by 2
-rotate column x=31 by 2
-rotate column x=28 by 1
-rotate column x=23 by 3
-rotate column x=22 by 3
-rotate column x=21 by 5
-rotate column x=20 by 1
-rotate column x=18 by 1
-rotate column x=17 by 3
-rotate column x=13 by 1
-rotate column x=10 by 1
-rotate column x=8 by 1
-rotate column x=7 by 5
-rotate column x=6 by 5
-rotate column x=5 by 1
-rotate column x=3 by 5
-rotate column x=2 by 5
-rotate column x=1 by 5

data/advent2017/input1.txt

@@ -1 +0,0 @@
-3294199471327195994824832197564859876682638188889768298894243832665654681412886862234525991553276578641265589959178414218389329361496673991614673626344552179413995562266818138372393213966143124914469397692587251112663217862879233226763533911128893354536353213847122251463857894159819828724827969576432191847787772732881266875469721189331882228146576832921314638221317393256471998598117289632684663355273845983933845721713497811766995367795857965222183668765517454263354111134841334631345111596131682726196574763165187889337599583345634413436165539744188866156771585647718555182529936669683581662398618765391487164715724849894563314426959348119286955144439452731762666568741612153254469131724137699832984728937865956711925592628456617133695259554548719328229938621332325125972547181236812263887375866231118312954369432937359357266467383318326239572877314765121844831126178173988799765218913178825966268816476559792947359956859989228917136267178571776316345292573489873792149646548747995389669692188457724414468727192819919448275922166321158141365237545222633688372891451842434458527698774342111482498999383831492577615154591278719656798277377363284379468757998373193231795767644654155432692988651312845433511879457921638934877557575241394363721667237778962455961493559848522582413748218971212486373232795878362964873855994697149692824917183375545192119453587398199912564474614219929345185468661129966379693813498542474732198176496694746111576925715493967296487258237854152382365579876894391815759815373319159213475555251488754279888245492373595471189191353244684697662848376529881512529221627313527441221459672786923145165989611223372241149929436247374818467481641931872972582295425936998535194423916544367799522276914445231582272368388831834437562752119325286474352863554693373718848649568451797751926315617575295381964426843625282819524747119726872193569785611959896776143539915299968276374712996485367853494734376257511273443736433464496287219615697341973131715166768916149828396454638596713572963686159214116763

data/advent2017/input13.txt

@@ -1,43 +0,0 @@
-0: 3
-1: 2
-2: 4
-4: 6
-6: 4
-8: 6
-10: 5
-12: 6
-14: 9
-16: 6
-18: 8
-20: 8
-22: 8
-24: 8
-26: 8
-28: 8
-30: 12
-32: 14
-34: 10
-36: 12
-38: 12
-40: 10
-42: 12
-44: 12
-46: 12
-48: 12
-50: 12
-52: 14
-54: 14
-56: 12
-62: 12
-64: 14
-66: 14
-68: 14
-70: 17
-72: 14
-74: 14
-76: 14
-82: 14
-86: 18
-88: 14
-96: 14
-98: 44

data/advent2017/input18.txt

@@ -1,41 +0,0 @@
-set i 31
-set a 1
-mul p 17
-jgz p p
-mul a 2
-add i -1
-jgz i -2
-add a -1
-set i 127
-set p 826
-mul p 8505
-mod p a
-mul p 129749
-add p 12345
-mod p a
-set b p
-mod b 10000
-snd b
-add i -1
-jgz i -9
-jgz a 3
-rcv b
-jgz b -1
-set f 0
-set i 126
-rcv a
-rcv b
-set p a
-mul p -1
-add p b
-jgz p 4
-snd a
-set a b
-jgz 1 3
-snd b
-set f 1
-add i -1
-jgz i -11
-snd a
-jgz f -16
-jgz a -19

data/advent2017/input19.txt

@@ -1,201 +0,0 @@
-                                                                                                                                                   |                                                     
-                         +-+             +-----------------------------+   +---+                                                           +-------+   +-+ +-+                   +-+     +-------+   +-+ 
-                         | |             |                             |   |   |                                                           |           | | | |                   | |     |       |   | | 
-           +-------------+ |   +-+     +-------------------------------|---|---|---------------------------------------------------------+ |           | | | |                   | |     |     +-+   | | 
-           |               |   | |     | |                             |   |   |                                                         | |           | | | |                   | |     |     |     | | 
-           |               |   | |     | |                 +-+   +---+ |   |   |         +-------------------------------------------------|-------------+ | |                   | |     |     |     | | 
-           |               |   | |     | |                 | |   |   | |   |   |         |                                               | |           |   | |                   | |     |     |     | | 
-   +-------|-------------------|-|-+   | |             +---+ I +-|---|-|---+   |         |                   +-------------------------------------------------------------------|-|-----|---+ +-------+ 
-   |       |               |   | | |   | |             |       | |   | |       |         |                   |                           | |           |   | |                   | |     |   |       |   
-   |       |               |   +---------|-------------|---------+ +-|---------|---------|-----------+       |                           | |     +---------|-|-------------------------------|-----+ |   
-   |       |               |     | |   | |             |       |   | | |       |         |           |       |                           | |     |     |   | |                   | |     |   |     | |   
-   |       |               |     | | +---|-------------|-------|---|-|-------------+     |           |       |                     +-------|-+   |     |   | +---------------------|-----|---+     | |   
-   |       |               |     | | | | |             |       |   | | |       |   |     |           |       |                     |     | | |   |     |   |                     | |     |         | |   
-   |       |               |     | | | | |             |       |   | | |   +---|---------|-----------|-------|---------------------|-------|-----------|-------------------------|-------|-------+ | |   
-   |       |               |     | | | | |             |       |   | | |   |   |   |     |           |       |                     |     | | |   |     |   |                     | |     |       | | |   
-   |       |               |     | | | | |             | +-----|---|-------|-------|-----|-----------------------------------------|---------|-------+ |   +---------------------|-|-------------|---+   
-   |       |               |     | | | | |             | |     |   | | |   |   |   |     |           |       |                     |     | | |   |   | |                         | |     |       | |     
-   |       |               |     | +-|-|---------------|-|-----|-----|-|---+   |   |     |           |       |                     |     | | |   |   | |       +-------------+   +-------|---+   | |     
-   |       |               |     |   | | |             | |     |   | | |       |   |     |           |       |                     |     | | |   |   | |       |             |     |     |   |   | |     
- +---------------------+ +-------|-----|---------------|-|-----|-----|-|-----------+     |           |       |           +-----------------|-----|-----|---------------------------|-----|-----+ | |     
- | |       |           | | |     |   | | |             | |     |   | | |       |         |           |       |           |         |     | | |   |   | |       |             |     |     |   | | | |     
- | |       |           | | |     |   | | |             | |     | +-|---|-------|---------------------|-------------------|---------|-----|-------|---|-|-------|-----------------------+ |   | | | |     
- | |       |           | | |     |   | | |             | |     | | | | |       |         |           |       |           |         |     | | |   |   | |       |             |     |   | |   | | | |     
- | |       |           | | |     |   | | |         +-----|---+ +-------|-----------------|-----------|-------+           |         | +---|-------------|---------------------|---------|-|-----+ | |     
- | |       |           | | |     |   | | |         |   | |   |   | | | |       |         |           |                   |         | |   | | |   |   | |       |             |     |   | |   |   | |     
- | | +-+ +-|-----------|-------------|-|-|---------------------+ | | +-|-----------------|-----------|---+     +---------|---------------|-|-|-----------------|-------------|-----|-----|---|---------+ 
- | | | | | |           | | |     |   | | |         |   | |   | | | |   |       |         |           |   |     |         |         | |   | | |   |   | |       |             |     |   | |   |   | |   | 
- | | | | | |           | | |     |   | | |         | +-|-|-+ | | | |   |       |         |           |   | +---|-----+   |         | |   | | |   |   | |       |       +-----|-----|-----|---+   | |   | 
- | | | | | |           | | |     |   | | |         | | | | | | | | |   |       |         |           |   | |   |     |   |         | |   | | |   |   | |       |       |     |     |   | |       | |   | 
- | | | | | +---+       | | |     |   | | |         +-|---|---|-|-----+ |   +-------------|-----------|---+ |   |     |   |         | |   | | |   |   | |       | +-----------------------|-+     | |   | 
- | | | | |     |       | | |     |   | | |           | | | | | | | | | |   |   |         |           |     |   |     |   |         | |   | | |   |   | |       | |     |     |     |   | | |     | |   | 
- | | | | |     |       | | |     |   | | |           | | | | | | | | | |   |   |         |   +---------------------------------------|---|---|---|---------------------|-------------------+     | |   | 
- | | | | |     |       | | |     |   | | |           | | | | | | | | | |   |   |         |   |       |     |   |     |   |         | |   | | |   |   | |       | |     |     |     |   | |       | |   | 
- | | | | |     |       | | |     |   | | |           | | | | | | | | | |   |   |         |   |       +-----|-+ |   +-----|-----------|---|-|-|-------------+ +---|-+   |     |     | +-----+     | |   | 
- | | | | |     |       | | |     |   | | |           | | | | | | | | | |   |   |         |   |             | | |   | |   |         | |   | | |   |   | |   | | | | |   |     |     | | | | |     | |   | 
- | | | | |     |       | | |     |   | | |           | | +-|-|-|---+ | |   |   |         |   |             | | |   | +-------------|-----------------|-|---|-|-|---|---------------|-|-|-|-----+ | |   | 
- | | | | |     |       | | |     |   | | |           | |   | | | |   | |   |   |         |   |             | | |   |     |         | |   | | |   |   | |   | | | | |   |     |     | | | | |   | | |   | 
- | | | | |     +---------|-|-----|-+ | | |           | |   | | | |   +-------------------|----------------------C--|---------------+ |   | | |   |   | |   | | +-------|-----|-----+ | | | |   | | |   | 
- | | | | |             | | |     | | | | |           | |   | | | |     |   |   |         |   |             | | |   |     |           |   | | |   |   | |   | |   | |   |     |       | | | |   | | |   | 
- | | | +-----------------|-------|-|---|-|-----------|-----|-|-|-|-----|-----------------|---|---------------------|-----|-----------|-------|-------|-----------|-----------|-----+ | | | | +-|-+ |   | 
- | | |   |             | | |     | | | | |           | |   | | | |     |   |   |         |   |             | | |   |     |           |   | | |   |   | |   | |   | |   |     |     | | | | | | |   |   | 
- | | |   |             | | |     | | | | |           | |   | | | |     |   |   |         |   |             | | |   |     |           |   | | |   |   | |   | |   | |   |     |     | +-|---|-+ |   |   | 
- | | |   |             | | |     | | | | |           | |   | | | |     |   |   |         |   |             | | |   |     |           |   | | |   |   | |   | |   | |   |     |     |   | | |   |   |   | 
- | | |   |             | | |     | | | +---------------------|---|---------|---------+   |   |             | | +---+     |           |   | | |   |   | |   | |   +-|-----------------+ | | | +-------+ | 
- | | |   |             | | |     | | |   |           | |   | | | |     |   |   |     |   |   |             | |           |           |   | | |   |   | |   | |     |   |     |     | | | | | | |   | | | 
- | | |   |             | | |     | | |   |           | |   | | | |     |   |   |     |   |   |             | |           |           |   | | |   |   | |   | |   +-|---------|-----|-|---+ | | |   | | | 
- | | |   |             | | |     | | |   |           | |   | | | |     |   |   |     |   |   |             | |           |           |   | | |   |   | |   | |   | |   |     |     | | |   | | |   | | | 
- | | |   |             | | |     | | |   |           | |   | | | | +---|---|-+ |     |   | +---+           | |           |           |   | | |   +-----|-----|---|-|-----------------|-----|---+   | | | 
- | | |   |             | | |     | | |   |           | |   | | | | |   |   | | |     |   | | | |           | |           |           |   | | |       | |   | |   | |   |     |     | | |   | |     | | | 
- | | |   |             | | |     | | |   |           +-|---|-------+   |   | | |     |   | | | |           | |           |           |   | | |       | |   | |   | |   |     |   +-|-|---------+   | | | 
- | | |   |             | | |     | | |   |             |   | | | |     |   | | |     |   | | | |           | |           |           |   | | |       | |   | |   | |   |     |   | | | |   | | |   | | | 
- | | |   |           +-|-----+   | | |   |             |   | | | |     |   | | |     |   | | | |           | |           |           |   | | |       | |   | +---|-|---|-----|---|-|-+ |   | | |   | | | 
- | | |   |           | | | | |   | | |   |             |   | | | |     |   | | |     |   | | | |           | |           |           |   | | |       | |   |     | |   |     |   | |   |   | | |   | | | 
- | | |   |           | | | | |   | | |   |     +-----+ +---------|---+ |   | | |     |   | | | |           | |           |           |   | | |       | |   |   +-|---+ |   +-----|---+ |   | | |   | | | 
- | | |   |           | | | | |   | | |   |     |     |     | | | |   | |   | | |     |   | | | |           | |           |           |   | | |       | |   |   | | | | |   | |   | | | |   | | |   | | | 
- | | |   |           | | | | |   | | |   |     |     |     | | | |   | |   | | |     |   | | | |           | |           |           |   | | |       | |   |   | | | | |   | |   | | | |   | | +-+ | | | 
- | | |   |           | | | | |   | | |   |     |     |     | | | |   | |   | | |     |   | | | |           | |           |           |   | | |       | |   |   | | | | |   | |   | | | |   | |   | | | | 
- +-+ |   |           | | | | |   | | |   |     |     |     | | | |   | |   | | |     |   | | | |           | |           |           |   | | |       | +---------|-|---------------------------+ | | | | 
-     |   |           | | | | |   | | |   |     |     |     | | | |   | |   | | |     |   | | | |           | |           |           |   | | |       |     |   | | | | |   | |   | | | |   | | | | | | | 
-     |   |           | | | | |   | | |   |     |     |     | | | |   | |   | | |     |   | | | |           | |           |     +-----------|-----------------------|---------------|-|-----|-----|-|-|-+ 
-     |   |           | | | | |   | | |   |     |     |     | | | |   | |   | | |     |   | | | |           | |           |     |     |   | | |       |     |   | | | | |   | |   | | | |   | | | | | |   
-     |   |           | | | | |   | | |   |     |     |     | | | |   | |   | | |     |   | | | |           | |           |     |     |   | | |       |     |   | | | | |   | |   | | | | +-|---|-|-+ |   
-     |   |           | | | | |   | | |   |     |     |     | | | |   | |   | | |     |   | | | |           | |           |     |     |   | | |       |     |   | | | | |   | |   | | | | | | | | |   |   
-     |   |           | | | | |   | | |   |     |     |     | | | |   | |   | | |     |   | | | |     +-----|-------------|-----|-----|-----|---------|---------|-|-|-|-------|-----|-+ | | | | | |   |   
-     |   |           | | | | |   | | |   |     |     |     | | | |   | |   | | |     |   | | | |     |     | |           |     |     |   | | |       |     |   | | | | |   | |   | |   | | | | | |   |   
-     |   |         +-------|-----|---|---|-----|-----|-----------|---|-|---|-|-|-----|-----|---------------|-|-----------|-----|-----|-----|---------|-----|-----|-|-|-----|-|-----|---|-|-------+   |   
-     |   |         | | | | | |   | | |   |     |     |     | | | |   | |   | | |     |   | | | |     |     | |           |     |     |   | | |       |     |   | | | | |   | |   | |   | | | | |     |   
-     |   |         | +-|---|---------|---|-------------------|-|-|---|-|---|-|-----------------|-----------|-|-----------|-----|-----|---------------------|-----------|---------|-----|---|---------|-+ 
-     |   |         |   | | | |   | | |   |     |     |     | | | |   | |   | | |     |   | | | |     |     | |           |     |     |   | | |       |     |   | | | | |   | |   | |   | | | | |     | | 
-     |   |         +---|---------|---|---|-----------|-----------------|---|---|------L----|-|-------+     | |           |     |     |   | | |       |     |   | +-|-|-|---|-|---|-----|-|---+ | +---+ | 
-     |   |             | | | |   | | |   |     |     |     | | | |   | |   | | |     |   | | | |           | |           |     |     |   | | |       |     |   |   | | |   | |   | |   | | |   | |     | 
-     |   |             | | | |   | | |   |     |     |     | | | |   | |   | | |     |   | | | |           | |           |     |     |   | | | +---------------------|-|-----|-----------|-------|---+ | 
-     |   |             | | | |   | | |   |     |     |     | | | |   | |   | | |     |   | | | |           | |           |     |     |   | | | |     |     |   |   | | |   | |   | |   | | |   | |   | | 
-     |   |             | | | |   | | |   |     |     |     | | | |   | |   | | |     |   | | +-|-----------|-|---+       | +-------------|-----------------|---|-----|-|---|-|-----|---|-|---+ | |   | | 
-     |   |             | | | |   | | |   |     |     |     | | | |   | |   | | |     |   | |   |           | |   |       | |   |     |   | | | |     |     |   |   | | |   | |   | |   | | | | | |   | | 
-     |   |             | | | |   | | |   |     |     |     | | | |   | |   | | |     |   | |   +-------------|---|-------|-----|---------|---|-|-----|-----------+ | | | +-|-------|-------|-----|---+ | 
-     |   |             | | | |   | | |   |     |     |     | | | |   | |   | | |     |   | |               | |   |       | |   |     |   | | | |     |     |   | | | | | | | |   | |   | | | | | |     | 
-     |   |             | | | |   | | |   |     |     |     | | | |   | |   | | |     |   | |               | |   |       | |   |   +-------|-|-------------|---|-+ | | | | | |   | |   | | | | | |     | 
-     |   |             | | | |   | | |   |     |     |     | | | |   | |   | | |     |   | |               | |   |       | |   |   | |   | | | |     |     |   |   | | | X | |   | |   | | | | | |     | 
-     |   |             | | | +---|-------|-----------------|---|-|-------------------|---------+           +-----|-------------|-----|-----|-----------------------|-|-------|---|-|---|-|-|-|-------+ | 
-     |   |             | | |     | | |   |     |     |     | | | |   | |   | | |     |   | |   |             |   |       | |   |   | |   | | | |     |     |   |   | | | | | |   | |   | | | | | |   | | 
-   +--B--|---------+   | | |     | | |   |     |     |     | | | |   | |   | | |     |   | |   |           +-|-----------|---+ |   | |   | | | |     |     |   | +-|---|---------+ |   | | | | | |   | | 
-   | |   |         |   | | |     | | |   |     |     |     | | | |   | |   | | |     |   | |   |           | |   |       | | | |   | |   | | | |     |     |   | | | | | | | |     |   | | | | | |   | | 
-   | |   |         +---|-|-----------|---------|-------------|-------|-----|-|-|-----|---|-----------------------|-------|-|-------|-|-----|---|-----|-----|---|-----|-----|-|-----|---+ | +-|-|-|---+ | 
-   | |   |             | | |     | | |   |     |     |     | | | |   | |   | | |     |   | |   |           | |   |       | | | |   | |   | | | |     |     |   | | | | | | | |     |     |   | | |     | 
-   | |   |             | | |     | | |   |     |     |     | | | |   | |   | | |     |   | |   |           +-----------------------|-------|-|-|---------------|-------|-|-------+ |     |   | | | +-+ | 
-   | |   |             | | |     | | |   |     |     |     | | | |   | |   | | |     |   | |   |             |   |       | | | |   | |   | | | |     |     |   | | | | | | | |   | |     |   | | | | | | 
-   | |   |             | | |     | | |   |     |     |     | | | |   | |   | | |     |   | |   |             |   |       | | | |   | |   | | | |     |     |   | | | | | | | |   | |     |   | | | | | | 
-   | |   |             | | |     | | |   |     |     |     | | | |   | |   | | |     |   | |   |             |   |       | | | |   | |   | | | |     |     |   | | | | | | | |   | |     |   | | | | | | 
-   | |   |             | | |     | | |   |     |     |     | | | |   +-----|-|-----------|-|---|-------------|---|-------|-----|---|-|---|-----|---------------|-----|-|-|-------|-|-------+ | | | | | | 
-   | |   |             | | |     | | |   |     |     |     | | | |     |   | | |     |   | |   |             |   |       | | | |   | |   | | | |     |     |   | | | | | | | |   | |     | | | | | | | | 
-   | |   +-------------|-|-|---------|---+     |     |     | | | |     |   | | |     |   | | +-|-----------------|-------+ | | |   | |   | | | |     |     |   | | +---|---------|-----+ | | | | | | | | 
-   | |                 | | |     | | |         |     |     | | | |     |   | | |     |   | | | |             |   |         | | |   | |   | | | |     |     |   | |   | | | | |   | |   | | | | | | | | | 
-   | |             +---|-|-|---------|---------------------|---|-------|-----|-|-----|---+ +---|-------------|---|-------------------------|-|-|-----------|---|---------|-|-|---|-|---|---+ | | | | | | 
-   | |             |   | | |     | | |         |     |     | | | |     |   | | |     |       | |             |   |         | | |   | |   | | | |     |     |   | |   | | | | |   | |   | |   | | | | | | 
-   | |             |   | | |     | | |         |     |     | | | |     |   | | |     |       | |         +---|---------------------------------------|---------|-|---|-|---|-----|-----------|-|-----+ | 
-   | |             |   | | |     | | |         |     |     | | | |     |   | | |     |       | |         |   |   |         | | |   | |   | | | |     |     |   | |   | | | | |   | |   | |   | | | |   | 
-   | |             |   +-|-|-----|-|-----------|-------------|-|-|---------|---|-----|-------|-----------|---|-------------+ | |   | |   | | | |     |     |   | +-----|-|---+   | | +-|-|-+ | | | |   | 
-   | |             |     | |     | | |         |     |     | | | |     |   | | |     |       | |         |   |   |           | |   | |   | | | |     |     |   |     | | | |     | | | | | | | | | |   | 
-   | |             |     | |     | | |         |     |     | | | |     |   | | |     |       | |         |   |   |           | |   | |   | | | |     |     |   |     | | | |     | | | | | | | | | |   | 
-   | |             |     | |     | | |         |     |     | | | |     |   | | |     |       | |         |   |   |           | |   | |   | | | |     |     |   |     | | | |     | | | | | | | | | |   | 
-   | |           +-------|-|-------|-------------------------|---------|---|---------------------------------|---------------------|-|---|-|---|-----|-----|-------------|-|-----|-|-|---|---+ | | |   | 
-   | |           | |     | |     | | |         |     |     | | | |     |   | | |     |       | |         |   |   |           | |   | |   | | | |     |     |   |     | | | |     | | | | | |   | | |   | 
-   | |           | |     | |     | | |         |     |     | | | |     |   | | |   +---------------------|---|-----------------|---------|-|---|---------------|---------|-------|---|---|-----------+ | 
-   | |           P |     | |     | | |         |     |     | | | |     |   | | |   | |       | |         |   |   |           | |   | |   | | | |     |     |   |     | | | |     | | | | | |   | | | | | 
-   | |           | |     | |     | | | +-------------|-----|---|-|-----+   | | |   | |       | |         |   |   |           | |   | |   | | | |     |     |   |     | | | +-----|-|-|-|---|---|---+ | | 
-   | |           | |     | |     | | | |       |     |     | | | |         | | |   | |       | |         |   |   |           | |   | |   | | | |     |     |   |     | | |       | | | | | |   | |   | | 
-   | |           | |     | |     | | | | +-----|-----|-------|---|-----------------|-------------------------|---------------|-|---|-------|---|-----|---------|-+   | | | +-----|-|-|---|---------+ | | 
-   | |           | |     | |     | | | | |     |     |     | | | |         | | |   | |       | |         |   |   |           | |   | |   | | | |     |     |   | |   | | | |     | | | | | |   | | | | | 
-   | |           | |     | |     | | | | |     |     |     | | | |         | | |   | |       | |         |   |   |           | |   | |   | | | |     |     |   | |   | | | |     | | +-|-|-----|---+ | | 
-   | |           | |     | |     | | | | |     |     |     | | | |         | | |   | |       | |         |   |   |           | |   | |   | | | |     |     |   | |   | | | |     | |   | | |   | |   | | 
-   | |           | |     | +---------|---+     | +---|-----|---|-|-------------|-----|-------|-|---------|---+   |       +-----|-----|-----|-|-|-------------+ | +---------|-------|---|-|-|-----|-+ | | 
-   | |           | |     |       | | | |       | |   |     | | | |         | | |   | |       | |         |       |       |   | |   | |   | | | |     |     | | |     | | | |     | |   | | |   | | | | | 
-   | |           | |     |       | | | |       +-+   |     | | | | +---------|-----|-|-------|-|-----+   |       |       |   | |   | |   | | | |     |     | | |     | | | |     | |   | | |   | | | | | 
-   | |           | |     |       | | | |             |     | | | | |       | | |   | |       | |     |   |       |       |   | |   | |   | | | |     |     | | |     | | | |     | |   | | |   | | | | | 
-   | |           | |     |       | | | |             |     | | | | |       | | |   | |       | |     +-----------|-----------|-----|-----|---|-|-----|---------|-----|-|-|-------|-|-+ | | |   | | | | | 
-   | |           | |     |       | | | |             |     | | | | |       | | |   | |       | |         |       |       |   | |   | |   | | | |     |     | | |     | | | |     | | | | | |   | | | | | 
-   | |           | |     |       | | | |             |     | | | | |       | | |   | |       | |         | +-------------------|-----|---|-|-|-------------|-----------|---|-----|---+ | | |   | | | | | 
-   | |           | |     |       | | | |             |     | | | | |       | | |   | |       | |         | |     |       |   | |   | |   | | | |     |     | | |     | | | |     | |   | | |   | | | | | 
-   +-|-------------------|---------|-|---------------|-----|-|-----|-------|-|-|-----+       | |         | |     |       |   | |   | |   | | | |     |     | | |     | | | |     | |   | | |   | | | | | 
-     |           | |     |       | | | |             |     | | | | |       | | |   |         | |         | |     |       |   | |   | |   | | | |     |     | | |     | | | |     | |   | | |   | | | | | 
-     |           | |     |       | | | |             |     | | | | |       | | |   |     +-----|------H------+   |       |   | |   | |   | | | |   +-|-----|---|-+   | | | +-+   | |   | | |   | | | | | 
-     |           | |     |       | | | |             |     | | | | |       | | |   |     |   | |         | | |   |       |   | |   | |   | | | |   | |     | | | |   | | |   |   | |   | | |   | | | | | 
-     |           | |     |       | | | |             |     | | | | |       | | |   |     |   | |         | | |   |       |   | |   | |   | | | |   | |     +-----|---|---------+ | |   +-|-+   | | | | | 
-     |           | |     |       | | | |             |     | | | | |       | | |   |     |   | |         | | |   |       |   | |   | |   | | | |   | |       | | |   | | |   | | | |     |     | | | | | 
-     |       +-----|-----|---------+ | |             |     | | | | |       | | |   |     |   | |         | | |   | +---------------|-----|-|---|-------------|---|-----|-|-----|-----------------+ | | | 
-     |       |   | |     |       |   | |             |     | | | | |       | | |   |     |   | |         | | |   | |     |   | |   | |   | | | |   | |       | | |   | | |   | | | |     |     |   | | | 
-     |       |   | |     |       |   | |             |     | | | | |       | | |   |     |   | |         | | |   | |     |   | |   | |   | | | |   | |       | | |   | | |   | | | |     |     |   | | | 
-     |       |   | |     |       |   | V             |     | | | | |       | | |   |     |   | |         | | |   | |     |   | |   | |   | | | |   | |       | | |   | | |   | | | |     |     |   | | | 
-   +-|-------------|-------+     |   | |             |     | | | | |       | | |   |     |   | |         | | |   | +---------------|-------|-+ |   | |       | | |   | | |   | | | |     |     |   | | | 
-   | |       |   | |     | |     |   | |             |     | | | | |       | | |   |     |   | |         | | |   |       |   | |   | |   | |   |   | |       | | |   | | |   | | | |     |     |   | | | 
-   | |       |   | |     | |     |   | |             |     | | | | |       | | |   |     | +-------------+ | |   |       |   | |   | |   | |   |   | |       | | |   | | |   | | | |     |     |   | | | 
-   | |       |   | |     | |     |   | |             |     | | | | |       | | |   |     | | | |           | |   |       |   | |   | |   | |   |   | |       | | |   | | |   | | | |     |     |   | | | 
- +-+ |       |   | |     | |     |   | +-------------|-------|---|-------+ | | |   |   +---|-|-|-----------|-|-------+   |   | |   | |   | |   |   | |       | | |   | | |   | | | |     |     |   | | | 
- |   |       |   | |     | |     |   |               |     | | | | |     | | | |   |   | | | | |           | |   |   |   |   | |   | |   | |   |   | |       | | |   | | |   | | | |     |     |   | | | 
- |   |     +-----|-|-------------|---|---------------|-------|---|-------|---|-----|---|---------------------|---|---|-------------------|-----|---|-|-------|-------|-------|-+ | |     |     |   | | | 
- |   |     | |   | |     | |     |   |               |     | | | | |     | | | |   |   | | | | |           | |   |   |   |   | |   | |   | |   |   | |       | | |   | | |   |   | |     |     |   | | | 
- |   |     | |   | |     | | +---|-------------------|---------+ | |     | | | |   |   +---+ | |         +-|-+   |   |   |   | |   | |   | |   |   | |   +---|---------|-|-----+ | |   +---------+ | | | 
- |   |     | |   | |     | | |   |   |               |     | |   | |     | | | |   |     |   | |         | |     |   |   |   | |   | |   | |   |   | |   |   | | |   | | |   | | | |   | |     | | | | | 
- |   |     | |   | | +-------|-------------------+   +---------+ | | +-----|---|---|-+   |   | |         | |     |   |   |   | | +---------|---|---------|---|-+ |   | | |   | | | +-+ | |     | | | | | 
- |   |     | |   | | |   | | |   |   |           |         | | | | | |   | | | |   | |   |   | |         | |     |   |   |   | | | | |   | |   |   | |   |   |   |   | | |   | | |   | | |     | | | | | 
- |   |     | |   | +-|-------|---|---+           +---------|-------------|-|-|-|-----|---|---|-|---------+ +-----|-----------------------------------|-----------|---|---|---|-|-------|-+     | | | | | 
- |   |     | |   |   |   | | |   |                         | | | | | |   | | | |   | |   |   | |                 |   |   |   | | | | |   | |   |   | |   |   T   |   | | |   | | |   | |       | | | | | 
- +---|-----|-|-------|-------|---------------------------------|---|---------|-|-----|---|-----------------------|---------------|-|-----|---+ |   | |   |   |   |   | | |   | | +-+ | |   +-+ | | | | | 
-     |     | |   |   |   | | |   |                         | | | | | |   | | | |   | |   |   | |                 |   |   |   | | | | |   | | | |   | |   |   |   |   | | |   | |   | | |   | | | | | | | 
-     |     | |   |   |   | | |   |                         +-----|-|-|-----|---|---------|---|-----------------------|-------|-|-----------|-|-|----------E------|-------|---|---+ | | |   | | | | | | | 
-     |     | |   |   |   | | |   |                           | | | | |   | | | |   | |   |   | |                 |   |   |   | | | | |   | | | |   | |   |   |   |   | | |   | | | | | |   | | | | | | | 
-     |     | +-------|-----------|---------------------------|-|-|---|---|-----------|---|-----+                 |   |   |   | | | | |   | | | |   | +---|-----------|---------|---+ | |   | | | | | | | 
-     |     |     |   |   | | |   |                           | | | | |   | | | |   | |   |   |                   |   |   |   | | | | |   | | | |   |     |   |   |   | | |   | | |   | |   | | | | | | | 
-     |     |     |   |   +-|-|-------------------------------|-|-|-------|-|---|---------|---------------+       |   +---------------|---|---------|---------------------|---+ | |   | | +-+ | | | | | | 
-     |     |     |   |     | |   |                           | | | | |   | | | |   | |   |   |           |       |       |   | | | | |   | | | |   |     |   |   |   | | |     | |   | | |   | | | | | | 
-     |     |     |   |     | | +---------------------------------|-|-|---|---|-|---|-|-------|-----------|-------|-----------|---|-------------|---|-----|---|---|-----|-|-------|---+ | +-+ | | | | | | 
-     |     |     |   |     | | | |                           | | | | |   | | | |   | |   |   |           |       |       |   | | | | |   | | | |   |     |   |   |   | | |     | |     |   | | | | | | | 
-     +-----+ +-----+ |     | | | |                           | | | | |   | | | |   | |   |   |       +---|-+     |       |   | | | | +-----|-------|---------|-----------|-----+ |     +---|-+ | | | | | 
-             |   | | |     | | | |                           | | | | |   | | | |   | |   |   |       |   | |     |       |   | | | |     | | | |   |     |   |   |   | | |       |         |   | | | | | 
- +---------------------------|---+                           | | | | |   | | | |   | +-------|-------|-----------|-------|---|-----------|-|---------------------|-----|-|---+   | +-------|-+ | | | | | 
- |           |   | | |     | | |                             | | | | |   | | | |   |     |   |       |   | |     |       |   | | | |     | | | |   |     |   |   |   | | |   |   | |       | | | | | | | 
- |           |   | | |     | | |                             | | | | |   | | | |   | +---|-----------|---|-|-----|-------|---|-|-----+   | | +-|---------|---|---------|-|---|-+ | |       +-+ | | | | | 
- |           |   | | |     | | |                             | | | | |   | | | |   | |   |   |       |   | |     |       |   | | | | |   | |   |   |     |   |   |   | | |   | | | |           | | | | | 
- +-----------|-----|-------|---|---------------------------------|-------|---|-------|---------------|-----------|---+   |   | | | | |   | |   |   +-----|-+ |   |   | | |   | | | |           | | | | | 
-             |   | | |     | | |                             | | | | |   | | | |   | |   |   |       |   | |     |   |   |   | | | | |   | |   |         | | |   |   | | |   | | | |           | | | | | 
- +---------------|-|-|---------|-----------------------------|-----|-|-------|-|---|-|---|---|-------|---------------|-------|---|-|-|---------|---+     | | |   |   | | |   | | | |           | | | | | 
- |           |   | | |     | | |                             | | | | |   | | | |   | |   |   |       |   | |     |   |   |   | | | | |   | |   |   |     | | |   |   | | |   | | | |           | | | | | 
- |           |   | | |   +-|---|-+ +-------------------------------+ |   | | | |   +-----|---|-------|---------------|-------|-------|---+ |   |   | +-----|-|---|-----------|-|---------------|---+ | | 
- |           |   | | |   | | | | | |                         | | |   |   | | | |     |   |   |       |   | |     |   |   |   | | | | |     |   |   | |   | | |   |   | | |   | | | |           | |   | | 
- +-----------|-----|-|---|-|---|-|---+                       | | |   |   | | | |     |   |   |       |   | |     +---|---|---|-|-|-+ |     |   |   | | +---|---------|-|-----|-|---|---+ +-----|---+ | | 
-             |   | | |   | | | | | | |                       | | |   |   | | | |     |   |   |       |   | |         |   |   | | |   |     |   |   | | | | | |   |   | | |   | | | |   | |     | | | | | 
-             |   | | |   | | | | | | |       +---------------|---|-------|---|-|-----|---|-----------|---|-|---------|-------|-|-|---+     |   |   +---+ | | |   | +-+ | +---|-------------+   | | | | | 
-             |   | | |   | | | | | | |       |               | | |   |   | | | |     |   |   |       |   | |         |   |   | | |         |   |     |   | | |   | |   |     | | | |   | | |   | | | | | 
-             |   | | |   | | | | | | |       |               | | |   |   | | | |     |   |   |       |   | +-------+ +-------|-----------------------------|---+ +-|-----------|-------+ | |   | | | | | 
-             |   | | |   | | | | | | |       |               | | |   |   | | | |     |   |   |       |   |         |     |   | | |         |   |     |   | | | |   |   |     | | | |     | |   | | | | | 
- +---+       |   | +-----|---------|---------|---------------|-------|-----|-+ |     |   |   |       |   +---------|-----|-------|-------------|---------|-|-----------|-----|---+ |   +-|-+   | | | | | 
- |   |       |   |   |   | | | | | | |       |               | | |   |   | |   |     |   |   |       |             |     |   | | |         |   |     |   | | | |   |   |     | |   |   | |     | | | | | 
- +---|-----+ |   |   |   | | | | | | |       |               | | |   |   +-|---|-----|---|-----------|-------+     +-----|---|-----------------|-----|-------|-|---------------|-------|---+   | | | | | 
-     |     | |   |   |   | | | | | | |       |               | | |   |     |   |     |   |   |       |       |           |   | | |         |   |     |   | | | |   |   |     | |   |   | | |   | | | | | 
-     |     | |   |   +---|---|-|-----|---+   |               | | |   |     +---------|---|-------------------------------------|-|-------------------------|-|---+ |   |     | | +-------|-|-------+ | | 
-     |     | |   |       | | | | | | |   |   |               | | |   |         |     |   |   |       |       |           |   | | |         |   |     |   | | | | | |   |     | | | |   | | |   | |   | | 
-     |     | |   |       | | | | | | |   |   |               | | |   |         |   +---------|---------------|-----------|---|-------------|---------------|-----|-----------|---------+ | +-+ | |   | | 
-     |     | |   |       | | | | | | |   |   |               | | |   |         |   | |   |   |       |       |           |   | | |         |   |     |   | | | | | |   |     | | | |     |   | | |   | | 
-     +-----|-----|---------+ | | | | +---+   |               | | +-----------------------|-----------------+ |           |   | | |         |   |     |   | | | | | +---------|---+ +-----|-+ | | |   | | 
-           | |   |       |   | | | |         |               | |     |         |   | |   |   |       |     | |           |   | | |         |   |     |   | | | | |     |     | |         | | | | |   | | 
-           | +---|-------|---|-+ | | +-------|---------------|-----------------------|---|---|-------------|-|-----------+   | | |         | +-------|---|-|-+ | | +---|-----|-----------|---|---+   | | 
-           |     |       |   |   | | |       |               | |     |         |   | |   |   |       |     | |               | | |         | | |     |   | |   | | |   |     | |         | | | |     | | 
-           |     |       |   |   | | |       |               | |     |         |   | |   |   |     +-|-----------------------+ | +-----------|---------------+ | | | +-|-----|-|-------+ | | | |     | | 
-           |     |       |   |   | | |       |               | |     |         |   | |   |   |     | |     | |                 |           | | |     |   | | | | | | | |     | |       | | | | |     | | 
-           +-----|-----------|-------|-------|---------------|-------|-------------+ |   +---+     +-|-----|-------------------|-------------|-|-----|---+ +-+ | | | | |     | | +---+ +-+ | | +---+ | | 
-                 |       |   |   | | |       |               | |     |         |     |               |     | |                 |           | | |     |         | | | | |     | | |   |     | |     | | | 
-                 |       |   +---+ | |       |               | |     |         |     +---------------|-----|-----------------------------------------|---------+ | | | +-------|-----------+ |     | | | 
-                 |       |         | |       |               | |     |         |                     |     | |                 |           | | |     |           | | |       | | |   |       |     | | | 
-                 |       +-----------|-------|---------------|-|-----|-------------------------------------|-------------------|-----------+ | +-----+ +-----------------------+ |   |       |     | | | 
-                 |                 | |       |               | |     |         |                     |     | |                 |             |         |         | | |       |   |   |       |     | | | 
-                 |                 +---------------------------|-----|-------------------------------|-------|-----------------|-------------+         +-------------|-------------+ +-------|---+ | | | 
-                 |                   |       |               | |     |         |                     |     | |                 |                                 | | |       |   | |         |   | | | | 
-                 +-------------------|-----------------------|-|-----|---------------------------------------------+ +---------|---------------------------+     | | |       +---|-+         |   | | | | 
-                                     |       |               | |     |         |                     |     | |     | |         |                           |     | | |           |           |   | | | | 
-                                     +-------+               +-+     +---------+                     +-------------+ +---------|---------------------------|-----|---------------|-----------+   +---|-+ 
-                                                                                                           | |                 |                           |     | | |           |                 | |   
-                                                                     +-------------------------------------+ +-----------------+                           +-----|-------------------------------+ | |   
-                                                                     |                                                                                           | | |           |               | | |   
-                                                                     +-------------------------------------------------------------------------------------------+ +-+           +---------------+ +-+   
-                                                                                                                                                                                                         

data/advent2017/input21.txt

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data/advent2017/input22.txt

@@ -1,25 +0,0 @@
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data/advent2017/input23.txt

@@ -1,32 +0,0 @@
-set b 99
-set c b
-jnz a 2
-jnz 1 5
-mul b 100
-sub b -100000
-set c b
-sub c -17000
-set f 1
-set d 2
-set e 2
-set g d
-mul g e
-sub g b
-jnz g 2
-set f 0
-sub e -1
-set g e
-sub g b
-jnz g -8
-sub d -1
-set g d
-sub g b
-jnz g -13
-jnz f 2
-sub h -1
-set g b
-sub g c
-jnz g 2
-jnz 1 3
-sub b -17
-jnz 1 -23

data/advent2017/input24.txt

@@ -1,57 +0,0 @@
-14/42
-2/3
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-0/30
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data/advent2017/input4.txt

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-idp zmrrzp zmrrzp nktp xsnx rjsxn
-eybrnib ivgntl vaxsbpi eybrnib
-nzvnq xvbfa pbhwwh ylju runvsj imlx vztesn
-nfdohd nfdohd gtevnky pivjyct ihvd fzcsrq lko fmqk
-kwpkks ecikxu bcxswlt qvrxm sbcqmh
-kdjrmj piuh kdjrmj vnaf gyedkg vptxgm xezssxx zsg qjzpo zsg
-oqo sley aqx qmpqb fgmylbj egd zivj kepxizv kuakyn lunbnd
-hmcf hmcf xlhgc hmcf cdlm buofnx
-onjcj yluonz kzmk phqo phqo phqo
-ohaafy efl bnkkjww wwjnyoj dxeaig ywnjjwo slk hrbebw ohlyju elf
-msohiqz aunk njki bfktdgi htmyrj mgx
-numlzrl rmnlulz glb ltt fhbajz gqxpu
-gko hco oai ryq xwy sdqosft spjkiu cxfhg ycwpglh noy rah
-btzpjem brpk vqr atxu rhlh rqv jmg fvyus
-phmxxgj ejx xje qtk hsb kqt npwj gqt
-hujyjp nwmsd ant zipuya lrkahww uwqal vzlo qmbo twkjkse ufivi
-zfbnyz fwvh xrnrw usn zin daq iwjzj
-yykyg iwypfy hehqnl cjvk cevdrec
-gui muuto wsta glqmx gfo rdmbv mxwz gffzt eejpw gion
-lpng nduid iqbpu nduid knrqd
-xwxn oefpckv gjaua ugaaj gjuaa
-qxk aeql trqdmqc crzlinj crzlinj trqdmqc rijcne ewyf
-rfv qmbe fvr bmeq
-upqyfw lowzq wpen upqyfw gfskbil sljuzh wpen
-bdcara qyhx rtaez qyq gbyr
-evzls qxtxq clzd svbgqi zxlzgss vtrre fko eebo qjyl
-zaapeo kpwhz tygknau nyd pch trp xqe
-ypzcafg rnqmbh qtteg sncu ssojhhm zonfym thir xmgheb wqj gpjg ssojhhm
-wvcwyn xrf muozyya lasdp xpjgu kpqv zkiihiv ifje cbdlavg xbied hfnaa
-qqqb rettz rycukl ihpkhh
-dnxzxqv znb znb fbxj azxtezb xvxa
-peqkd xlzqkov esgnw ucku hrwpfxd xtd vnig vlmfp ajte qswr kqoj
-dpwy oavzkk dwyp ehij upqxgii pydw
-amfc hfv xmqa nqvn cal rqmcq oej amqx cla ntxj
-hqhhe qkbhwli wmhlcq xaczs peywuo
-vcr xfv xfv kymo qpszwzo xfv
-nmrbur tswo xbo ljlrzo bmhpgc pev zovkznz lok wbbhtkk
-tojj lxqgr rhjavrm ndsdup gdbjwaq cqpnl wfaxivl rfry ryfr udspnd
-beffod sknlph amb feobdf
-mldgn jxovw yuawcvz kzgzwht rxqhzev fsdnvu vluuo eycoh cugf qjugo
-tlnd qcxj ker fdir cgkpo nrqhyq raef uqadf iahy rxx
-mhvisju lhmdbs tcxied xeidtc ujry cditex gvqpqm
-cgc jazrp crgnna uvuokl uvuokl uoiwl sknmc sknmc
-rvbu czwpdit vmlihg spz lfaxxev zslfuto oog dvoksub

data/latlong.htm

@@ -1,86 +1,6 @@
-<HTML>
-<BODY>
-<TITLE>Latitude-Longitude of US Cities (www.realestate3d.com)</TITLE>
+Latitude-Longitude of US Cities (www.realestate3d.com)
 
-<H2>Latitude-Longitude of US Cities (www.realestate3d.com)</H2>
-<BR> 
-
-Notes:
-<UL>
-<LI> Lat-long database valuable to the GPSer. Some gotten 
-     from the defunct http://rs560.cl.msu.edu/weather/stations/
-<LI> <A HREF="world-latlong.htm">Latitude & longitude of World cities
-     </A>
-<LI> <A HREF="uslatlongdegmin.htm">Version of US city lat-long 
-     but with degrees/minutes/seconds information</A>
-<LI> <A HREF="airport.htm">Latitude and Longitude of US Airports
-     (work in progress) </A>
-<LI> <A HREF="usmap.htm">Very primitive Java-based Map
-     (work in progress) </A>
-<LI> <A HREF="http://www.realestate3d.com"> Back to main page </A>
-</UL>
-
-<HR>
-<H3>United States</H3>
-
-<UL>
-<LI> Alabama
-<LI> Alaska
-<LI> Arizona
-<LI> Arkansas
-<LI> California
-<LI> Colorado
-<LI> Connecticut
-<LI> Delaware
-<LI> District of Columbia
-<LI> Florida
-<LI> Georgia
-<LI> Hawaii
-<LI> Idaho
-<LI> Illinois
-<LI> Indiana
-<LI> Iowa
-<LI> Kansas
-<LI> Kentucky
-<LI> Louisiana
-<LI> Maine
-<LI> Maryland
-<LI> Massachusetts
-<LI> Michigan
-<LI> Minnesota
-<LI> Mississippi
-<LI> Missouri
-<LI> Montana
-<LI> Nebraska
-<LI> Nevada
-<LI> New Hampshire
-<LI> New Jersey
-<LI> New Mexico
-<LI> New York
-<LI> North Carolina
-<LI> North Dakota
-<LI> Ohio
-<LI> Oklahoma
-<LI> Oregon
-<LI> Pennsylvania
-<LI> Rhode Island
-<LI> South Carolina
-<LI> South Dakota
-<LI> Tennessee
-<LI> Texas
-<LI> Utah
-<LI> Vermont
-<LI> Virginia
-<LI> Washington
-<LI> West Virginia
-<LI> Wisconsin
-<LI> Wyoming
-</UL>
-
-
-<PRE>
-
-ID     LAT    LON     Location
+ID     LAT    LON     Location,State
 
 Alabama
 
@@ -1458,18 +1378,3 @@ Wyoming
 [WRL]  43.97  107.97  Worland,WY
 [P60]  44.55  110.42  Yellowstone,WY
 
-</PRE>
-
-<HR>
-<P>
-<FONT SIZE=-1><I>
-Find out more about RealEstate3D.com,
- email <A HREF= "mailto:info@realestate3d.com">
- info@realestate3d.com</A>.<BR>
-Copyright &copy; 1996-1997 Orogo Technologies</I></FONT>
-</CENTER>
-<P>
-
-</BODY>
-</HTML>
-

ipynb/Advent-2025-AI.ipynb

@@ -9,7 +9,7 @@
     "\n",
     "# Advent of Code 2025: The AI LLM Edition\n",
     "\n",
-    "*This notebook shows some solutions by Gemini, Claude, and ChatGPT, three AI Large Language Models (LLMs),  for the 2025 [**Advent of Code**](https://adventofcode.com/) (AoC) programming puzzles. In order to understand each puzzle, you'll have to look at the problem descriptions at [**Advent of Code**](https://adventofcode.com/2025) for each [**Day**](https://adventofcode.com/2025/day/1), and you can also look at [**my solutions**](Advent2025.ipynb), which I did before asking the LLMs for theirs.*\n",
+    "*This notebook shows some solutions by Gemini, Claude, and ChatGPT, three AI Large Language Models (LLMs),  for the 2025 [**Advent of Code**](https://adventofcode.com/) (AoC) programming puzzles. In order to understand each puzzle, you'll have to look at the problem descriptions at [**Advent of Code**](https://adventofcode.com/2025) for each [**Day**](https://adventofcode.com/2025/day/1), and you can also look at [**my solutions**](Advent2025.ipynb), which I did before asking the LLMs for theirs. TLDR: the LLMs did great, got all the problems right, did so very quickly, but their code was 5 times more verbose and ran 3 times slower than mine.*\n",
     "\n",
     "*All the code in this notebook is written by an LLM (except for the one line where I call the LLM's code for each puzzle). My comments (like this one) are in italics, and my prompts given to the LLMs are in **bold italics**. Sometimes I quote the LLM's responses; those are in* regular roman font.\n",
     "\n",
@@ -331,7 +331,7 @@
     "    It seems I made a subtle logic error in my previous calculation for the Right (R) rotation.\n",
     "    When the dial is at 0, the distance to the *next* zero is **100**, not 0.\n",
     "\n",
-    "*which is exactly the error I made on *my* first attempt! Gemini produced the following updated code:*"
+    "*which is exactly the error I made on **my** first attempt! Gemini produced the following updated code:*"
    ]
   },
   {

ipynb/Cryptarithmetic.ipynb

@@ -8,32 +8,32 @@
     "\n",
     "# Cryptarithmetic Problems\n",
     "\n",
-    "On 28 April 2014 Gary Antonik had a [Numberplay column](https://web.archive.org/web/20191001030614/https://wordplay.blogs.nytimes.com/2014/04/28/num/) that quotes my friend [Bill Gosper](https://en.wikipedia.org/wiki/Bill_Gosper). (Gosper often presents more advanced puzzles in the [math-fun](http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun) mailing list.)  This puzzle was:\n",
+    "On 28 April 2014 Gary Antonik had a [Numberplay column](https://web.archive.org/web/20191001030614/https://wordplay.blogs.nytimes.com/2014/04/28/num/) in which my friend [Bill Gosper](https://en.wikipedia.org/wiki/Bill_Gosper) poses this puzzle:\n",
     "\n",
-    "> For the expression  `N U M + B E R = P L A Y`,\n",
-    "> - Which distinct numerals (each different) can be substituted for letters to make a valid expression?\n",
-    "> - How many solutions are there?\n",
+    "<hr>\n",
+    "\n",
+    "**For the expression  N U M + B E R = P L A Y**,\n",
+    "- **Which distinct numerals (each different) can be substituted for letters to make a valid expression?**\n",
+    "- **How many solutions are there?**\n",
+    "<hr>\n",
     "\n",
     "I [tackled](https://www.udacity.com/wiki/cs212/unit-2#rethinking-eval) this type of problem (also known as a [cryptarithmetic](http://mathworld.wolfram.com/Cryptarithmetic.html) or [alphametic](http://mathworld.wolfram.com/Alphametic.html) or [verbal arithmetic](https://en.wikipedia.org/wiki/Verbal_arithmetic) problem) in my Udacity class [CS 212](https://www.udacity.com/wiki/cs212/unit-2#cryptarithmetic). \n",
     "\n",
     "\n",
     "\n",
-    "![](https://www.azquotes.com/picture-quotes/quote-when-in-doubt-use-brute-force-ken-thompson-131-46-05.jpg)\n",
+    "My initial approach follows Ken Thompson's adage,  \"when in doubt, use brute force\":\n",
     "\n",
-    "My initial approach follows Ken Thompson's adage,  \"when in doubt, use brute force.\"\n",
-    "\n",
-    "- There are only 10 factorial or 3.6 million permutations of 10 digits, so we can try them all.\n",
+    "- There are only 10 factorial (3.6 million) permutations of 10 digits, so we can try them all.\n",
     "- For each permutation, substitute the digits for the corresponding letters in the formula.\n",
     "- Use Python's `eval` function to check if the resulting formula is a valid, true expression. \n",
-    "- Report the one(s) that are.\n",
+    "- Report the expressions that are.\n",
     "\n",
-    "The basic idea is simple, but there are a few complications to worry about:\n",
+    "The basic idea is simple, but there are a few complications:\n",
     "\n",
-    "- Python uses `==` for equality and `**` for exponentiation, but math notation  uses `=` and `^`.   I'll accept any of these, and translate from math to Python with `to_python`.\n",
+    "- Python uses `==` for equality and `**` for exponentiation, but math notation uses `=` and `^`.   I'll define `to_python` to handle this.\n",
     "- A number with a leading zero digit (like `012`) is illegal (except that `0` by itself is ok).\n",
-    "- We'll have to catch divide-by-zero errors, as in `1/0` or `4/(3-2-1)`.\n",
+    "- We'll have to catch divide-by-zero errors, as in  `4/(3-2-1)`.\n",
     "- In general, it is **unsafe** to eval a string that comes from a user, because a malicious user could inject malware. But eval-ing strings that we make ourselves is no worse than running code that we make ourselves. \n",
-    "- Only uppercase letters are replaced by digits. So in `2 * B or not 2 * BE`, the `or` and `not` are Python keywords.\n",
     "- Should I define a `solve` function to find one solution (faster) or all solutions (comprehensive)? I'll handle both use cases by defining `solve` to  yield solutions one at a time. You can quickly get the first one with `first` or all of them with `set`. \n",
     "\n",
     "# Defining `solve`\n",
@@ -49,12 +49,12 @@
    },
    "outputs": [],
    "source": [
-    "from typing import Iterable, Callable, Tuple\n",
+    "from typing import Iterable, Callable\n",
     "from itertools import permutations\n",
+    "from collections import Counter\n",
     "import re\n",
     "\n",
-    "Formula  = str # A formula in Math notation, like \"NUM ^ BER = PLAY\"\n",
-    "Pformula = str # A formula in Python notation, like \"NUM ** BER == PLAY\"\n",
+    "Formula  = str # A formula in Math notation, like \"NUM + BER = PLAY\"\n",
     "Solution = str # A formula with letters relaced by digits, like \"356 + 742 = 1098\""
    ]
   },
@@ -62,7 +62,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Below we see that `solve` works by substituting each permutation of digits for the letters in the formula, and then reporting on the ones that are valid (ones that evaluate to true and have no number with a leading zero). Note that `solve` checks if a `to_python` version of the  formula is `valid`, and if it is, returns a substituted version of the original formula."
+    "Below we see that `solve` works by substituting each permutation of digits for the letters in the formula, and then reporting on the ones that are valid. "
    ]
   },
   {
@@ -76,29 +76,29 @@
     "def solve(formula) -> Iterable[Solution]:\n",
     "    \"\"\"Given a formula like 'NUM + BER == PLAY', fill in digits to solve it.\"\"\"\n",
     "    letters  = all_letters(formula)\n",
-    "    pformula = to_python(formula)\n",
+    "    pyformula = to_python(formula)\n",
     "    for digits in permutations('1234567890', len(letters)):\n",
-    "        if valid(subst(digits, letters, pformula)):\n",
+    "        if valid(subst(digits, letters, pyformula)):\n",
     "            yield subst(digits, letters, formula)\n",
     "        \n",
-    "def subst(digits, letters, formula) -> Formula:\n",
+    "def subst(digits: str, letters: str, formula: Formula) -> Formula:\n",
     "    \"\"\"Substitute digits for letters in formula.\"\"\"\n",
     "    return formula.translate(str.maketrans(letters, cat(digits)))\n",
     "        \n",
-    "def valid(pformula) -> bool:\n",
-    "    \"\"\"A pformula is valid iff it has no leading zero, and evaluates to True.\"\"\"\n",
+    "def valid(pyformula: Formula) -> bool:\n",
+    "    \"\"\"A pyformula is valid iff it has no leading zero, and evaluates to True.\"\"\"\n",
     "    try:\n",
-    "        return (not leading_zero(pformula)) and (eval(pformula) is True)\n",
+    "        return (not leading_zero(pyformula)) and (eval(pyformula) is True)\n",
     "    except ArithmeticError:\n",
     "        return False\n",
     "    \n",
-    "def to_python(formula: Formula) -> Pformula:\n",
+    "def to_python(formula: Formula) -> Formula:\n",
     "    \"\"\"Convert ' = ' and '^' to ' == ' and '**'.\"\"\"\n",
     "    return formula.replace(' = ', ' == ').replace('^', '**') \n",
     "\n",
-    "def all_letters(formula: str) -> str: \n",
-    "    \"\"\"The set of letters in formula, in the form of an alphabetized string.\"\"\"\n",
-    "    return cat(sorted(set(re.findall('[A-Z]', formula))))\n",
+    "def all_letters(formula: Formula) -> str: \n",
+    "    \"\"\"The set of letters in formula, in the order they first appear.\"\"\"\n",
+    "    return cat(Counter(re.findall('[A-Z]', formula)))\n",
     "\n",
     "def first(iterable): \"First element\"; return next(iter(iterable), None)\n",
     "    \n",
@@ -111,7 +111,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "It would be good to have some unit tests for these functions, but I moved them to the end of this notebook, so that we can go right ahead and solve the problem:"
+    "We can go right ahead and solve the problem:"
    ]
   },
   {
@@ -127,7 +127,7 @@
     {
      "data": {
       "text/plain": [
-       "'587 + 439 = 1026'"
+       "'246 + 789 = 1035'"
       ]
      },
      "execution_count": 3,
@@ -160,8 +160,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 16.9 s, sys: 19.2 ms, total: 17 s\n",
-      "Wall time: 17 s\n"
+      "CPU times: user 11.1 s, sys: 14 ms, total: 11.1 s\n",
+      "Wall time: 11.1 s\n"
      ]
     },
     {
@@ -176,7 +176,7 @@
     }
    ],
    "source": [
-    "%time solutions = set(solve('NUM + BER = PLAY'))\n",
+    "%time solutions = list(solve('NUM + BER = PLAY'))\n",
     "len(solutions)"
    ]
   },
@@ -184,7 +184,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "It takes 15 or 20 seconds to find 96 solutions, Here are ten of them:"
+    "It takes about 11 seconds to find 96 solutions, Here are ten of them:"
    ]
   },
   {
@@ -195,16 +195,16 @@
     {
      "data": {
       "text/plain": [
-       "['452 + 637 = 1089',\n",
-       " '589 + 437 = 1026',\n",
-       " '879 + 426 = 1305',\n",
-       " '749 + 286 = 1035',\n",
-       " '756 + 342 = 1098',\n",
-       " '673 + 425 = 1098',\n",
-       " '439 + 587 = 1026',\n",
-       " '432 + 657 = 1089',\n",
-       " '423 + 675 = 1098',\n",
-       " '429 + 876 = 1305']"
+       "['246 + 789 = 1035',\n",
+       " '249 + 786 = 1035',\n",
+       " '264 + 789 = 1053',\n",
+       " '269 + 784 = 1053',\n",
+       " '284 + 769 = 1053',\n",
+       " '286 + 749 = 1035',\n",
+       " '289 + 746 = 1035',\n",
+       " '289 + 764 = 1053',\n",
+       " '324 + 765 = 1089',\n",
+       " '325 + 764 = 1089']"
       ]
      },
      "execution_count": 5,
@@ -213,7 +213,7 @@
     }
    ],
    "source": [
-    "list(solutions)[:10]"
+    "solutions[:10]"
    ]
   },
   {
@@ -247,34 +247,180 @@
     {
      "data": {
       "text/plain": [
-       "         3028913 function calls in 3.011 seconds\n",
+       "         3127170 function calls (3127152 primitive calls) in 2.079 seconds\n",
        "\n",
        "   Ordered by: internal time\n",
        "\n",
        "   ncalls  tottime  percall  cumtime  percall filename:lineno(function)\n",
-       "   309270    1.779    0.000    1.833    0.000 {built-in method builtins.eval}\n",
-       "   453271    0.229    0.000    0.229    0.000 {method 'translate' of 'str' objects}\n",
-       "   453270    0.220    0.000    0.220    0.000 {method 'search' of 're.Pattern' objects}\n",
-       "        2    0.215    0.107    3.065    1.532 89248256.py:1(solve)\n",
-       "   453271    0.209    0.000    0.669    0.000 89248256.py:9(subst)\n",
-       "   453271    0.146    0.000    0.146    0.000 {built-in method maketrans}\n",
-       "   453270    0.128    0.000    2.182    0.000 89248256.py:13(valid)\n",
-       "   453272    0.084    0.000    0.084    0.000 {method 'join' of 'str' objects}\n",
-       "        1    0.000    0.000    3.065    3.065 89248256.py:28(first)\n",
-       "        1    0.000    0.000    3.065    3.065 {built-in method builtins.exec}\n",
-       "        1    0.000    0.000    0.000    0.000 89248256.py:24(all_letters)\n",
-       "        1    0.000    0.000    0.000    0.000 {method 'findall' of 're.Pattern' objects}\n",
-       "        1    0.000    0.000    0.000    0.000 re.py:233(findall)\n",
-       "        1    0.000    0.000    0.000    0.000 89248256.py:20(to_python)\n",
-       "        1    0.000    0.000    0.000    0.000 {built-in method builtins.sorted}\n",
-       "        1    0.000    0.000    0.000    0.000 re.py:289(_compile)\n",
-       "        1    0.000    0.000    3.065    3.065 {built-in method builtins.next}\n",
-       "        1    0.000    0.000    0.000    0.000 {built-in method builtins.isinstance}\n",
-       "        2    0.000    0.000    0.000    0.000 {method 'replace' of 'str' objects}\n",
+       "   355667    1.382    0.000    1.411    0.000 {built-in method builtins.eval}\n",
+       "   461238    0.155    0.000    0.155    0.000 {method 'translate' of 'str' objects}\n",
+       "   461238    0.128    0.000    0.413    0.000 1816288747.py:9(subst)\n",
+       "   461237    0.104    0.000    0.104    0.000 {method 'search' of 're.Pattern' objects}\n",
+       "   461238    0.092    0.000    0.092    0.000 {built-in method maketrans}\n",
+       "   461237    0.074    0.000    1.589    0.000 1816288747.py:13(valid)\n",
+       "        1    0.068    0.068    1.383    1.383 1816288747.py:1(solve)\n",
+       "   461239    0.037    0.000    0.037    0.000 {method 'join' of 'str' objects}\n",
+       "      9/1    0.024    0.003    1.905    1.905 {built-in method builtins.next}\n",
+       "      2/0    0.005    0.003    0.000          base_events.py:1954(_run_once)\n",
+       "        1    0.002    0.002    0.043    0.043 socket.py:700(send_multipart)\n",
+       "        1    0.002    0.002    0.020    0.020 history.py:92(only_when_enabled)\n",
+       "      354    0.001    0.000    0.002    0.000 ipkernel.py:775(_clean_thread_parent_frames)\n",
+       "        1    0.001    0.001    0.013    0.013 history.py:1024(writeout_cache)\n",
+       "       11    0.001    0.000    0.012    0.001 socket.py:623(send)\n",
+       "      177    0.000    0.000    0.001    0.000 threading.py:1477(enumerate)\n",
+       "     1416    0.000    0.000    0.000    0.000 threading.py:1110(ident)\n",
+       "        3    0.000    0.000    0.050    0.017 events.py:87(_run)\n",
+       "      708    0.000    0.000    0.000    0.000 {method 'keys' of 'dict' objects}\n",
+       "        3    0.000    0.000    0.000    0.000 attrsettr.py:66(_get_attr_opt)\n",
+       "        1    0.000    0.000    0.043    0.043 zmqstream.py:573(_handle_events)\n",
+       "  460/456    0.000    0.000    0.000    0.000 {built-in method builtins.isinstance}\n",
+       "      354    0.000    0.000    0.000    0.000 {method 'values' of 'dict' objects}\n",
+       "      2/0    0.000    0.000    0.000          {method 'control' of 'select.kqueue' objects}\n",
        "        1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}\n",
-       "        1    0.000    0.000    0.000    0.000 {built-in method builtins.iter}\n",
+       "      179    0.000    0.000    0.000    0.000 {method '__exit__' of '_thread.RLock' objects}\n",
+       "        1    0.000    0.000    0.000    0.000 {method 'execute' of 'sqlite3.Connection' objects}\n",
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        "        1    0.000    0.000    0.000    0.000 <string>:1(<module>)\n",
-       "        1    0.000    0.000    0.000    0.000 {built-in method builtins.len}"
+       "        1    0.000    0.000    0.000    0.000 {method 'cancelled' of '_asyncio.Future' objects}\n",
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+       "        1    0.000    0.000    0.000    0.000 iostream.py:255(closed)"
       ]
      },
      "metadata": {},
@@ -316,7 +462,7 @@
    },
    "outputs": [],
    "source": [
-    "def translate_formula(formula, verbose=False) -> Tuple[str, str]:\n",
+    "def translate_formula(formula: Formula) -> tuple[str, str]:\n",
     "    \"\"\"Translate formula into two values: (lambda function string, parameter letters).\"\"\"\n",
     "    letters  = all_letters(formula)\n",
     "    assert len(letters) <= 10, f'{len(letters)} letters is too many; only 10 allowed'\n",
@@ -368,8 +514,8 @@
     {
      "data": {
       "text/plain": [
-       "('lambda A,B,E,L,M,N,P,R,U,Y: N and B and P and (100*N + 10*U + M) + (100*B + 10*E + R) == (1000*P + 100*L + 10*A + Y)',\n",
-       " 'ABELMNPRUY')"
+       "('lambda N,U,M,B,E,R,P,L,A,Y: N and B and P and (100*N + 10*U + M) + (100*B + 10*E + R) == (1000*P + 100*L + 10*A + Y)',\n",
+       " 'NUMBERPLAY')"
       ]
      },
      "execution_count": 9,
@@ -415,7 +561,7 @@
     {
      "data": {
       "text/plain": [
-       "'587 + 439 = 1026'"
+       "'246 + 789 = 1035'"
       ]
      },
      "execution_count": 11,
@@ -448,20 +594,20 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 1.11 s, sys: 3.16 ms, total: 1.11 s\n",
-      "Wall time: 1.11 s\n"
+      "CPU times: user 476 ms, sys: 1.66 ms, total: 478 ms\n",
+      "Wall time: 477 ms\n"
      ]
     }
    ],
    "source": [
-    "%time solutions2 = set(faster_solve('NUM + BER = PLAY'))"
+    "%time solutions2 = list(faster_solve('NUM + BER = PLAY'))"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "About 15 times faster! Does it give the same solutions as `solve`?"
+    "About 20 times faster! Does it give the same solutions as `solve`?"
    ]
   },
   {
@@ -553,7 +699,7 @@
     "SORRY + TO + BE + A + PARTY = POOPER\n",
     "SORRY + TO + BUST + YOUR = BUBBLE\n",
     "STEEL + BELTED = RADIALS\n",
-    "ABRA + CADABRA + ABRA + CADABRA = HOUDINI\n",
+    "2 * (ABRA + CADABRA) = HOUDINI\n",
     "I + GUESS + THE + TRUTH = HURTS\n",
     "LETS + CUT + TO + THE = CHASE\n",
     "THATS + THE + THEORY = ANYWAY\n",
@@ -570,6 +716,10 @@
     "sum(range(POP)) = BOBO\n",
     "ODD + ODD = EVEN\n",
     "ROMANS+ALSO+MORE+OR+LESS+ADDED = LETTERS\n",
+    "X * X * X = M\n",
+    "XXVI + CCCXXXI = CCCLVII\n",
+    "LXVII + CCCLXXX = CDXLVII\n",
+    "CXX * XLII = MMMMMXL\n",
     "FOUR+ONE = FIVE and ONE+ONE+ONE+ONE+ONE = FIVE\n",
     "TEN+SEVEN+SEVEN+SEVEN+FOUR+FOUR+ONE = FORTY\n",
     "NINETEEN+THIRTEEN+THREE+2*TWO+3*ONE = FORTYTWO\n",
@@ -594,251 +744,263 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "NUM + BER = PLAY\n",
-      "587 + 439 = 1026\n",
-      "__________________________________________________________________________________________\n",
+      "246 + 789 = 1035\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "YOU = ME ^ 2\n",
-      "576 = 24 ^ 2\n",
-      "__________________________________________________________________________________________\n",
+      "289 = 17 ^ 2\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "SEND + MORE = MONEY\n",
       "9567 + 1085 = 10652\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "FOUR + SCORE + 7 = YEARS + AGO\n",
-      "9071 + 26014 + 7 = 34512 + 580\n",
-      "__________________________________________________________________________________________\n",
+      "6071 + 29014 + 7 = 34512 + 580\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "WRONG + WRONG = RIGHT\n",
-      "37081 + 37081 = 74162\n",
-      "__________________________________________________________________________________________\n",
+      "12734 + 12734 = 25468\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "WRIGHT + WRIGHT = TO * FLY + FLIGHT\n",
       "413058 + 413058 = 82 * 769 + 763058\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "HALF + HALF = WHOLE\n",
       "9604 + 9604 = 19208\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "HALF + FIFTH + TENTH + TENTH + TENTH = WHOLE\n",
       "6701 + 14126 + 25326 + 25326 + 25326 = 96805\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "BASE + BALL = GAMES\n",
       "7483 + 7455 = 14938\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "YOUR + YOU = HEART\n",
       "9426 + 942 = 10368\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "EAT + THAT = APPLE\n",
       "819 + 9219 = 10038\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "ALPHABET + LETTERS = SCRABBLE\n",
       "17531908 + 7088062 = 24619970\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "POTATO + TOMATO = PUMPKIN\n",
       "168486 + 863486 = 1031972\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "ODD * ODD = FREAKY\n",
       "677 * 677 = 458329\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "DOUBLE + DOUBLE + TOIL = TROUBLE\n",
       "798064 + 798064 + 1936 = 1598064\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "WASH + YOUR = HANDS\n",
-      "5291 + 6748 = 12039\n",
-      "__________________________________________________________________________________________\n",
+      "4261 + 7835 = 12096\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "WEAR + A + MASK + WASH = SAFER\n",
-      "9617 + 1 + 3125 + 9124 = 21867\n",
-      "__________________________________________________________________________________________\n",
+      "2743 + 4 + 9416 + 2410 = 14573\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "PERSON + WOMAN + MAN = CAMERA\n",
       "320567 + 96817 + 817 = 418201\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "TWO + TWENTY = TWELVE + TEN\n",
-      "784 + 781279 = 781351 + 712\n",
-      "__________________________________________________________________________________________\n",
+      "123 + 124617 = 124594 + 146\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "AA + BB + CC = ABC\n",
       "11 + 99 + 88 = 198\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "PI * R^2 = AREA\n",
       "96 * 7^2 = 4704\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "A^2 + B^2 = C^2\n",
       "3^2 + 4^2 = 5^2\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "A^2 + BE^2 = BY^2 \n",
       "5^2 + 12^2 = 13^2 \n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "AYH^2 + BEE^2 = SEE^2\n",
       "760^2 + 522^2 = 922^2\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "RAMN = R^3 + RM^3 = N^3 + RX^3\n",
       "1729 = 1^3 + 12^3 = 9^3 + 10^3\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "MON-EY = EVIL^(1/2)\n",
-      "108-42 = 4356^(1/2)\n",
-      "__________________________________________________________________________________________\n",
+      "132-58 = 5476^(1/2)\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "SIN^2 + COS^2 = UNITY\n",
       "235^2 + 142^2 = 75389\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "SPEED + LIMIT = FIFTY\n",
-      "40221 + 36568 = 76789\n",
-      "__________________________________________________________________________________________\n",
+      "10224 + 73635 = 83859\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "TERRIBLE + NUMBER = THIRTEEN\n",
       "45881795 + 302758 = 46184553\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "SEVEN + SEVEN + SIX = TWENTY\n",
       "68782 + 68782 + 650 = 138214\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "EIGHT + EIGHT + TWO + ONE + ONE = TWENTY\n",
       "52371 + 52371 + 104 + 485 + 485 = 105816\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "ELEVEN + NINE + FIVE + FIVE = THIRTY\n",
       "797275 + 5057 + 4027 + 4027 = 810386\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "NINE + SEVEN + SEVEN + SEVEN = THIRTY\n",
       "3239 + 49793 + 49793 + 49793 = 152618\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "FOURTEEN + TEN + TEN + SEVEN = FORTYONE\n",
       "19564882 + 482 + 482 + 78082 = 19643928\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "HAWAII + IDAHO + IOWA + OHIO = STATES\n",
       "510199 + 98153 + 9301 + 3593 = 621246\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "VIOLIN * 2 + VIOLA = TRIO + SONATA\n",
       "176478 * 2 + 17645 = 2076 + 368525\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "SEND + A + TAD + MORE = MONEY\n",
       "9283 + 7 + 473 + 1062 = 10825\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "ZEROES + ONES = BINARY\n",
       "698392 + 3192 = 701584\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "DCLIZ + DLXVI = MCCXXV\n",
       "62049 + 60834 = 122883\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "COUPLE + COUPLE = QUARTET\n",
       "653924 + 653924 = 1307848\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "FISH + N + CHIPS = SUPPER\n",
       "5718 + 3 + 98741 = 104462\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "SATURN + URANUS + NEPTUNE + PLUTO = PLANETS\n",
       "127503 + 502351 + 3947539 + 46578 = 4623971\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "PLUTO not in {PLANETS}\n",
-      "63985 not in {6314287}\n",
-      "__________________________________________________________________________________________\n",
+      "12345 not in {1267849}\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "EARTH + AIR + FIRE + WATER = NATURE\n",
       "67432 + 704 + 8046 + 97364 = 173546\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "TWO * TWO = SQUARE\n",
-      "807 * 807 = 651249\n",
-      "__________________________________________________________________________________________\n",
+      "567 * 567 = 321489\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "HIP * HIP = HURRAY\n",
       "958 * 958 = 917764\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "NORTH / SOUTH = EAST / WEST\n",
       "51304 / 61904 = 7260 / 8760\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "NAUGHT ^ 2 = ZERO ^ 3\n",
       "328509 ^ 2 = 4761 ^ 3\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "I + THINK + IT + BE + THINE = INDEED\n",
       "1 + 64125 + 16 + 73 + 64123 = 128338\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "DO + YOU + FEEL = LUCKY\n",
       "57 + 870 + 9441 = 10368\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "WELL - DO + YOU = PUNK\n",
-      "5277 - 13 + 830 = 6094\n",
-      "__________________________________________________________________________________________\n",
+      "1399 - 65 + 750 = 2084\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "NOW + WE + KNOW + THE = TRUTH\n",
       "673 + 38 + 9673 + 128 = 10512\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "SORRY + TO + BE + A + PARTY = POOPER\n",
       "80556 + 20 + 34 + 9 + 19526 = 100145\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "SORRY + TO + BUST + YOUR = BUBBLE\n",
       "94665 + 24 + 1092 + 5406 = 101187\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "STEEL + BELTED = RADIALS\n",
       "87336 + 936732 = 1024068\n",
-      "__________________________________________________________________________________________\n",
-      "ABRA + CADABRA + ABRA + CADABRA = HOUDINI\n",
-      "7457 + 1797457 + 7457 + 1797457 = 3609828\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
+      "2 * (ABRA + CADABRA) = HOUDINI\n",
+      "2 * (7457 + 1797457) = 3609828\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "I + GUESS + THE + TRUTH = HURTS\n",
       "5 + 26811 + 478 + 49647 = 76941\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "LETS + CUT + TO + THE = CHASE\n",
       "9478 + 127 + 75 + 704 = 10384\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "THATS + THE + THEORY = ANYWAY\n",
       "86987 + 863 + 863241 = 951091\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "TWO + TWO = FOUR\n",
       "734 + 734 = 1468\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "X / X = X\n",
       "1 / 1 = 1\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "X + X = X\n",
       "0 + 0 = 0\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "A^N + B^N = C^N and N > 1\n",
       "3^2 + 4^2 = 5^2 and 2 > 1\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "ATOM^0.5 = A + TO + M\n",
       "1296^0.5 = 1 + 29 + 6\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "ALL + GLITTERS is not GOLD\n",
-      "166 + 46500389 is not 4762\n",
-      "__________________________________________________________________________________________\n",
+      "122 + 32455678 is not 3920\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "ONE < TWO and FOUR < FIVE\n",
-      "351 < 703 and 2386 < 2491\n",
-      "__________________________________________________________________________________________\n",
+      "123 < 451 and 6178 < 6903\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "ONE < TWO < THREE < TWO * TWO\n",
-      "431 < 674 < 62511 < 674 * 674\n",
-      "__________________________________________________________________________________________\n",
+      "123 < 451 < 46733 < 451 * 451\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "(2 * BE or not 2 * BE) = THE + QUES-TION\n",
-      "(2 * 13 or not 2 * 13) = 843 + 7239-8056\n",
-      "__________________________________________________________________________________________\n",
+      "(2 * 13 or not 2 * 13) = 793 + 6438-7205\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "sum(range(AA)) = BB\n",
       "sum(range(11)) = 55\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "sum(range(POP)) = BOBO\n",
       "sum(range(101)) = 5050\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "ODD + ODD = EVEN\n",
       "655 + 655 = 1310\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "ROMANS+ALSO+MORE+OR+LESS+ADDED = LETTERS\n",
       "975348+3187+5790+79+1088+36606 = 1022098\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
+      "X * X * X = M\n",
+      "2 * 2 * 2 = 8\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
+      "XXVI + CCCXXXI = CCCLVII\n",
+      "3370 + 1113330 = 1116700\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
+      "LXVII + CCCLXXX = CDXLVII\n",
+      "20133 + 8882000 = 8902133\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
+      "CXX * XLII = MMMMMXL\n",
+      "422 * 2633 = 1111126\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "FOUR+ONE = FIVE and ONE+ONE+ONE+ONE+ONE = FIVE\n",
       "1380+345 = 1725 and 345+345+345+345+345 = 1725\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "TEN+SEVEN+SEVEN+SEVEN+FOUR+FOUR+ONE = FORTY\n",
       "520+12820+12820+12820+4937+4937+902 = 49756\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "NINETEEN+THIRTEEN+THREE+2*TWO+3*ONE = FORTYTWO\n",
       "42415114+56275114+56711+2*538+3*841 = 98750538\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "IN + ARCTIC + TERRAIN + AN + ANCIENT + EERIE + ICE + TRACT + I + ENTER + A + TRANCE = FLATIANA\n",
       "42 + 379549 + 5877342 + 32 + 3294825 + 88748 + 498 + 57395 + 4 + 82587 + 3 + 573298 = 10354323\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "ONE < TWO < THREE < SEVEN - THREE < THREE + TWO < THREE + THREE < SEVEN < SEVEN + ONE < THREE * THREE\n",
-      "321 < 483 < 45711 < 91612 - 45711 < 45711 + 483 < 45711 + 45711 < 91612 < 91612 + 321 < 45711 * 45711\n",
-      "__________________________________________________________________________________________\n",
+      "123 < 451 < 46733 < 93832 - 46733 < 46733 + 451 < 46733 + 46733 < 93832 < 93832 + 123 < 46733 * 46733\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "ABCDEFGHIJ/JIHGFEDCBA = AI/IG\n",
       "1073589264/4629853701 = 16/69\n",
-      "__________________________________________________________________________________________\n",
+      "——————————————————————————————————————————————————————————————————————————————————————————\n",
       "AN + ACCELERATING + INFERENTIAL + ENGINEERING + TALE + ELITE + GRANT + FEE + ET + CETERA = ARTIFICIAL + INTELLIGENCE\n",
       "59 + 577404251698 + 69342491650 + 49869442698 + 1504 + 40614 + 82591 + 344 + 41 + 741425 = 5216367650 + 691400684974\n",
-      "CPU times: user 42.1 s, sys: 77.8 ms, total: 42.2 s\n",
-      "Wall time: 42.2 s\n"
+      "CPU times: user 18.2 s, sys: 47.4 ms, total: 18.2 s\n",
+      "Wall time: 18.2 s\n"
      ]
     },
     {
      "data": {
       "text/plain": [
-       "79"
+       "83"
       ]
      },
      "execution_count": 15,
@@ -847,7 +1009,7 @@
     }
    ],
    "source": [
-    "def show(formulas: Iterable[Formula], sep='_'*90):\n",
+    "def show(formulas: Iterable[Formula], sep='—'*90):\n",
     "    \"\"\"Solve all the formulas and show results.\"\"\"\n",
     "    for f in formulas:\n",
     "        print(f'{sep}\\n{f}\\n{first(faster_solve(f))}')\n",
@@ -902,8 +1064,8 @@
     "\n",
     "assert translate_formula(\"A + B = CD\") == ('lambda A,B,C,D: C and (A) + (B) == (10*C + D)', 'ABCD')\n",
     "assert translate_formula(\"NUM + BER = PLAY\") == (\n",
-    "    'lambda A,B,E,L,M,N,P,R,U,Y: N and B and P and (100*N + 10*U + M) + (100*B + 10*E + R) == (1000*P + 100*L + 10*A + Y)',\n",
-    "    'ABELMNPRUY')"
+    "    'lambda N,U,M,B,E,R,P,L,A,Y: N and B and P and (100*N + 10*U + M) + (100*B + 10*E + R) == (1000*P + 100*L + 10*A + Y)',\n",
+    "    'NUMBERPLAY')"
    ]
   }
  ],
@@ -923,7 +1085,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.15"
+   "version": "3.13.3"
   }
  },
  "nbformat": 4,

ipynb/Stubborn.ipynb

@@ -7,24 +7,24 @@
    "source": [
     "<div style=\"text-align: right\">Peter Norvig<br>Mar 2024</div> \n",
     "\n",
-    "# Stubborn Number Endings\n",
+    "# Stubborn Number Endings (e.g. 5² = 25)\n",
     "\n",
-    "[Francis Su](https://www.francissu.com/)'s book *Mathematics for Human Flourishing* mentions the fact that numbers that end in \"5\" have a square that also ends in \"5\". \n",
+    "[Francis Su](https://www.francissu.com/)'s fine book *[Mathematics for Human Flourishing](https://www.francissu.com/flourishing)* mentions the fact that numbers that end in \"5\" have a square that also ends in \"5\". \n",
     "\n",
     "For example, 5² = 25, 15² = 225, and 25² = 625. \n",
     "\n",
     "This leads to some questions:\n",
     "\n",
-    "- Is there an easy way to calculate the square of a number ending in \"5\"?\n",
+    "- Is there an easy way to calculate the square of a number ending in \"5\" without using a calculator?\n",
     "- What should we call this property of \"square has same ending\"?\n",
     "- Are there other digits besides 5 that have this  property?\n",
-    "- Can we prove the property, not just show some examples?\n",
     "- Are there multi-digit endings that have this property?\n",
+    "- Can we prove it, not just show some examples?\n",
     "\n",
     "\n",
     "## Is there an easy way to calculate the square of a number ending in \"5\"?\n",
     "\n",
-    "Let's make a table of {number: square} pairs and try to see a pattern:"
+    "Let's make a table of {number: square} pairs and look for a pattern:"
    ]
   },
   {
@@ -111,36 +111,34 @@
     "\n",
     "## What should we call this property?\n",
     "\n",
-    "Let's define an **ending** as the rightmost-digits (zero or more) of a number in decimal notation. \n",
+    "Let's define an **ending** as the rightmost-digits of an integer in decimal notation. \n",
     "\n",
-    "Then we can say that an ending is **stubborn**  if every number with that ending has a square with the same ending.\n",
+    "Then we can say that an ending is **stubborn**  if every integer with that ending has  the same ending when squared.\n",
     "\n",
     "## Are there other digits besides 5 that are stubborn?\n",
     "\n",
-    "We could work this out in our heads, or with paper and pencil, or we can compute it with an expression:"
+    "We could work this out in our heads, or with paper and pencil, or we can compute it:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
-   "id": "c86f99ed-48fa-4954-9467-b72d67252d73",
+   "execution_count": 3,
+   "id": "ddcdafa8-bfa6-4707-951c-6683701e06c2",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "{'0', '1', '5', '6'}"
+       "{0, 1, 5, 6}"
       ]
      },
-     "execution_count": 15,
+     "execution_count": 3,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "digits = '0123456789'\n",
-    "\n",
-    "{e for e in digits if str(int(e) ** 2).endswith(e)}"
+    "{e for e in range(10) if str(e ** 2).endswith(str(e))}"
    ]
   },
   {
@@ -152,23 +150,27 @@
     "\n",
     "## Can we prove stubborness?\n",
     "\n",
-    "We have seen that 0² ends in 0, 1² ends in 1, 5² ends in 5, and 6² ends in 6. And we have checked some numbers with those endings, for example, 245² ends in 5. But can we **prove** that **every** number ending in 0, 1, 5, or 6 has a square that ends in the same digit?\n",
+    "We have seen that 0² ends in 0, 1² ends in 1, 5² ends in 5, and 6² ends in 6. And we have checked some numbers with those endings, for example, 245² ends in 5. But can we **prove** that **every** integer ending in 0, 1, 5, or 6 has a square that ends in the same digit?\n",
     "\n",
-    "Some notation: I'll use quote marks, as in \"*se*\" to mean the string of staring digits \"*s*\" followed by the string of ending digits \"*e*\".\n",
+    "Some notation: I'll use quote marks, as in \"*se*\" to mean the string of starting digits \"*s*\" followed by the string of ending digits \"*e*\".\n",
     "\n",
     "With a little bit of algebra we can see that if *s* is any string of digits and *e* is a single ending digit,  then:\n",
     "\n",
-    "\"*se*\"² = (10⋅*s* + *e*)² = (10⋅*s*)² + 2⋅(10⋅*s* ⋅ *e*) + *e*² = 10 ⋅ (10⋅*s*² + 2⋅*s*⋅*e*) + *e*²\n",
+    "\"*se*\"² = (10⋅*s* + *e*)² = (10⋅*s*)² + 2⋅(10⋅*s*⋅*e*) + *e*² = 10 ⋅ (10⋅*s*² + 2⋅*s*⋅*e*) + *e*² = *e*² (mod 10)\n",
     "\n",
-    "This is ten times some integer, plus *e*², so \"*se*\"² ends in the digit *e* if and only if *e*² ends in *e*, and we know that is true for 0, 1, 5, and 6, and for no other digits.\n",
+    "In other words, \"*se*\"² is 10 times some integer plus *e*², so \"*se*\"² ends in the digit *e* if and only if *e*² ends in *e*. \n",
+    "\n",
+    "We know that is true for 0, 1, 5, and 6, and for no other digits.\n",
     "\n",
     "## Are there multi-digit endings that are stubborn?\n",
     "\n",
     "The algebraic argument above can be extended to work with an ending string *e* that is *k* digits long:\n",
     "\n",
-    "\"*se*\"² = (10<sup>*k*</sup>⋅*s* + *e*)² = (10<sup>*k*</sup>⋅*s*)² + 2⋅(10<sup>*k*</sup>⋅*s* ⋅ *e*) + *e*² = 10<sup>*k*</sup> ⋅ (10<sup>*k*</sup>⋅*s*² + 2⋅*s*⋅*e*) + *e*²\n",
+    "\"*se*\"² = (10<sup>*k*</sup>⋅*s* + *e*)² = (10<sup>*k*</sup>⋅*s*)² + 2⋅(10<sup>*k*</sup>⋅*s* ⋅ *e*) + *e*² = 10<sup>*k*</sup> ⋅ (10<sup>*k*</sup>⋅*s*² + 2⋅*s*⋅*e*) + *e*² = *e*² (mod 10)\n",
     "\n",
-    "This is 10<sup>*k*</sup> times some integer, plus *e*², so again \"*se*\"² ends in *e* if and only if *e*² ends in *e*. To put it another way, to test whether *e* is stubborn, all we have to do is square *e* and see if the result ends in *e*. There is one complication: we'd like to say that \"00\" is stubborn, because any number ending in \"00\", when squared, also ends in \"00\", for example 200² = 40000. But 00² is zero, which we write as \"0\", not as \"00\" or \"0000\". To make sure that \"00\" is considered stubborn, I will define the predicate function `stubborn(ending)` to test the square of \"1\" followed by the ending (I could have chosen any other starting digit string and the result would be the same). \n"
+    "Again, \"*se*\"² ends in *e* if and only if *e*² ends in *e*. To test whether *e* is a stubborn ending (with all possible starting digit strings), all we have to do is square *e* and see if the result ends in *e*. \n",
+    "\n",
+    "There is one **complication**: we'd like to say that \"0\" and \"00\" are two distinct stubborn endings, but 0 and 00 are the same integer. To distinguish them, I will describe endings as strings, not integers. I will define the predicate function `stubborn(ending: str)`:"
    ]
   },
   {
@@ -179,8 +181,10 @@
    "outputs": [],
    "source": [
     "def stubborn(ending: str) -> bool:\n",
-    "    \"\"\"Does the square of any number with this ending also end with this ending?\"\"\"\n",
-    "    return str(int(\"1\" + ending) ** 2).endswith(ending)"
+    "    \"\"\"Does every integer with this ending, when squared, also end with this ending?\"\"\"\n",
+    "    start  = \"1\" # Arbitrary choice of start; could be any non-zero digit string\n",
+    "    square = str(int(start + ending) ** 2)\n",
+    "    return square.endswith(ending)"
    ]
   },
   {
@@ -193,7 +197,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 5,
    "id": "57e64e31-0674-4849-bf72-f6c6b437009a",
    "metadata": {},
    "outputs": [
@@ -203,13 +207,16 @@
        "['00', '01', '25', '76']"
       ]
      },
-     "execution_count": 17,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "[s + e for s in digits for e in digits if stubborn(s + e)]"
+    "digits  = '0123456789'\n",
+    "endings = [s + e for s in digits for e in digits]\n",
+    "\n",
+    "list(filter(stubborn, endings))"
    ]
   },
   {
@@ -217,12 +224,12 @@
    "id": "61a2b8e2-2bdf-458f-adaf-ffde56125862",
    "metadata": {},
    "source": [
-    "We could easily continue on in this way, enumerating all three-, four- or even six-digit endings, and checking each one to see if it is stubborn.  There are only a million six-digit endings. But there are a quadrillion 15-digit endings, so it would take a *long* time to check all of those. And 100-digit endings? Forget about it.  Instead we need to rely on a simplification:\n",
+    "We could easily continue on in this way, enumerating all three-, four-, or more-digit endings, and checking each one to see if it is stubborn.  There are only a million possible six-digit endings; we could quickly check them all. But there are a quadrillion 15-digit endings, so it would take a *long* time to check all of those. And 100-digit endings? Forget about it.  Instead we need to rely on an optimization:\n",
     "- Any two-digit stubborn ending ('00', '01', '25', '76') has to end in a one-digit-stubborn ending ('0', '1', '5', '6').\n",
     "- In general, any *d*-digit stubborn ending has to end in a (*d*-1)-digit stubborn ending.\n",
-    "- So, to find the stubborn endings of length 100, I don't need to generate and test all 10<sup>100</sup> endings, I only need to consider the stubborn endings of length 99 and check each one of them. (If this simplification is not obvious, stop and convince yourself it is true.)\n",
+    "- So, to find the stubborn endings of length 100, I don't need to generate and test all 10<sup>100</sup> endings, I only need to consider the stubborn endings of length 99, prepend each of the ten digits to each of these endings to get a list of 100-digit endings, and then check each one for stubborness. \n",
     "\n",
-    "Using this simplification we can efficiently compute all stubborn-endings of a given length *d* as follows (caching greatly improves efficiency):"
+    "Using this optimization we can efficiently compute all stubborn-endings of a given length *d* as follows (caching greatly improves efficiency):"
    ]
   },
   {
@@ -232,17 +239,16 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "from functools import lru_cache\n",
+    "from functools import cache\n",
     "\n",
-    "@lru_cache(None)\n",
-    "def stubborn_endings(d: int) -> list:\n",
+    "@cache\n",
+    "def stubborn_endings(d: int) -> list[str]:\n",
     "    \"\"\"A list of all stubborn endings of length `d` digits.\"\"\"\n",
     "    if d == 0:\n",
-    "        return [''] # The empty ending is the sole stubborn ending of length 0.\n",
+    "        return [''] # The empty ending is the only stubborn ending of length 0.\n",
     "    else:\n",
-    "        return [(s + e) for e in stubborn_endings(d - 1) \n",
-    "                        for s in digits \n",
-    "                        if stubborn(s + e)]"
+    "        endings = [s + e for e in stubborn_endings(d - 1) for s in digits]\n",
+    "        return list(filter(stubborn, endings))"
    ]
   },
   {
@@ -262,7 +268,16 @@
     {
      "data": {
       "text/plain": [
-       "['000', '001', '625', '376']"
+       "{0: [''],\n",
+       " 1: ['0', '1', '5', '6'],\n",
+       " 2: ['00', '01', '25', '76'],\n",
+       " 3: ['000', '001', '625', '376'],\n",
+       " 4: ['0000', '0001', '0625', '9376'],\n",
+       " 5: ['00000', '00001', '90625', '09376'],\n",
+       " 6: ['000000', '000001', '890625', '109376'],\n",
+       " 7: ['0000000', '0000001', '2890625', '7109376'],\n",
+       " 8: ['00000000', '00000001', '12890625', '87109376'],\n",
+       " 9: ['000000000', '000000001', '212890625', '787109376']}"
       ]
      },
      "execution_count": 7,
@@ -271,76 +286,13 @@
     }
    ],
    "source": [
-    "stubborn_endings(3)"
+    "{d: stubborn_endings(d) for d in range(10)}"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 8,
-   "id": "d1dc31eb-e5dd-405e-b16d-eceef5c9493c",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['0000', '0001', '0625', '9376']"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "stubborn_endings(4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "id": "81730e6b-7218-4fca-9107-2a9539f62ea3",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['00000', '00001', '90625', '09376']"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "stubborn_endings(5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "id": "288506c8-6dc1-40d5-842a-eb65ed94ae98",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['000000', '000001', '890625', '109376']"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "stubborn_endings(6)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "id": "73491ea5-a4c8-4221-8fc7-d6ce44d17bb4",
+   "id": "38c26d56-d916-481e-bc04-51af7a52b1e8",
    "metadata": {},
    "outputs": [
     {
@@ -352,7 +304,7 @@
        " '6046992680891830197061490109937833490419136188999442576576769103890995893380022607743740081787109376']"
       ]
      },
-     "execution_count": 11,
+     "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -366,26 +318,26 @@
    "id": "37a45341-8dac-4720-be7d-388fa47eec1a",
    "metadata": {},
    "source": [
-    "## More questions!\n",
-    "\n",
     "This leads to a few new questions.\n",
     "\n",
-    "## Can each stubborn ending be extended exactly one way?\n",
+    "## Can each stubborn ending always be extended exactly one way?\n",
     "\n",
-    "We know that each stubborn ending of length *d* has to build on the endings of length *d - 1*, but is it always the case that for any length *d* there will be exactly four endings? Might there be a case where two digits work with one of the endings, or no digits?\n",
-    "\n",
-    "I can show that there are always 4 endings up to length *d* = 2000, but I leave it to you to describe a proof that this will always be true."
+    "There are four stubborn endings of length 1: '0', '1', '5', and '6'. So far, every time we try, each of the four can be extended from length *d* to length *d*+1 in exactly one way. Will that always be the case? I leave it up to you to provide a proof, but I can show that it is true for every *d* up to 2000:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 9,
    "id": "654d53af-e58f-4ed2-874b-c4573f3a9a7a",
    "metadata": {},
    "outputs": [],
    "source": [
+    "def last_digits(endings) -> list[str]: \n",
+    "    \"\"\"A list of the last digits of these endings.\"\"\"\n",
+    "    return [e[-1] for e in endings]\n",
+    "    \n",
     "for d in range(1, 2000):\n",
-    "    assert len(stubborn_endings(d)) == 4 "
+    "    assert last_digits(stubborn_endings(d)) == ['0', '1', '5', '6']"
    ]
   },
   {
@@ -393,37 +345,45 @@
    "id": "537556a3-d570-4a50-93bf-9632b40f9b47",
    "metadata": {},
    "source": [
-    "One cool implication: if it is true that a stubborn ending of any length can always be extended, that means there is an infinitely long integer whose square ends with itself!\n",
-    "\n",
     "## What digits are used to extend each ending?\n",
     "\n",
-    "There doesn't seem to be a pattern, and all digits seemingly get used roughly evenly. \n",
-    "\n",
-    "I don't have a theory of which digit comes next, but I can count how many times each digit appears in the 2000-digit endings that end in \"5\" and \"6\", and see that each of the ten digits appears about 200 times:"
+    "I don't have a theory of which digit is used to extend each stubborn ending, but I can count:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 10,
    "id": "4dbd7ace-8b41-4ea7-b71f-8f7e318243e1",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Counter({'0': 205,\n",
-       "         '3': 173,\n",
-       "         '2': 208,\n",
-       "         '6': 197,\n",
-       "         '9': 198,\n",
-       "         '5': 197,\n",
-       "         '4': 206,\n",
-       "         '8': 214,\n",
-       "         '7': 205,\n",
-       "         '1': 197})"
+       "{'0': Counter({'0': 1999}),\n",
+       " '1': Counter({'0': 1999}),\n",
+       " '5': Counter({'8': 214,\n",
+       "          '2': 208,\n",
+       "          '4': 206,\n",
+       "          '0': 205,\n",
+       "          '7': 205,\n",
+       "          '9': 198,\n",
+       "          '6': 197,\n",
+       "          '1': 197,\n",
+       "          '5': 196,\n",
+       "          '3': 173}),\n",
+       " '6': Counter({'1': 214,\n",
+       "          '7': 208,\n",
+       "          '5': 206,\n",
+       "          '9': 205,\n",
+       "          '2': 205,\n",
+       "          '0': 198,\n",
+       "          '3': 197,\n",
+       "          '8': 197,\n",
+       "          '4': 196,\n",
+       "          '6': 173})}"
       ]
      },
-     "execution_count": 13,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -431,47 +391,23 @@
    "source": [
     "from collections import Counter\n",
     "\n",
-    "zero, one, five, six = stubborn_endings(2000)\n",
-    "\n",
-    "Counter(five)"
+    "{end: Counter(start) for (*start, end) in stubborn_endings(2000)}"
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": 14,
-   "id": "96bdab37-c5a3-4597-b4ca-fb560e4c3163",
+   "cell_type": "markdown",
+   "id": "35e84df9-0b76-4d8d-aa13-2c4e73a86643",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "Counter({'9': 205,\n",
-       "         '6': 174,\n",
-       "         '7': 208,\n",
-       "         '3': 197,\n",
-       "         '0': 198,\n",
-       "         '4': 196,\n",
-       "         '5': 206,\n",
-       "         '1': 214,\n",
-       "         '2': 205,\n",
-       "         '8': 197})"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
    "source": [
-    "Counter(six)"
+    "This is saying that the stubborn endings \"0\" and \"1\" are always extended by prepending a \"0\", but for \"5\" and \"6\", it seems to be pretty random; each of the ten digits appears roughly 200 times."
    ]
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
+   "display_name": "Python [conda env:base] *",
    "language": "python",
-   "name": "python3"
+   "name": "conda-base-py"
   },
   "language_info": {
    "codemirror_mode": {
@@ -483,7 +419,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.15"
+   "version": "3.13.9"
   }
  },
  "nbformat": 4,

ipynb/TruncatablePrimes.ipynb

@@ -13,11 +13,11 @@
     "\n",
     "[![](https://community.wolfram.com//c/portal/getImageAttachment?filename=IMG_20181212_120939.jpg&userId=143131)](https://community.wolfram.com/groups/-/m/t/1569707)\n",
     "\n",
-    "The 24-digit number printed on it is a prime, and as you sharpen the pencil and remove digits one at a time from the left, the resulting numbers are all primes:\n",
+    "The 24-digit number printed on this pencil is a prime, and as you sharpen the pencil and remove digits one at a time from the left, the resulting numbers are all primes:\n",
     "\n",
     "    357686312646216567629137 is prime\n",
     "     57686312646216567629137 is prime\n",
-    "      7686312646216567629137 is prime|\n",
+    "      7686312646216567629137 is prime\n",
     "                 ...\n",
     "                         137 is prime\n",
     "                          37 is prime\n",
@@ -1127,7 +1127,7 @@
     "\n",
     "# Note on Modular Exponentiation\n",
     "\n",
-    "Just one more thing: none of this would work unless we can efficiently compute *a*<sup>(*n* - 1)</sup> (mod *n*).  How does the `pow` builtin function do it? When *a* and *n* are 24-digit numbers, if we naively tried to compute `a ** (n - 1)`, we'd have two problems: we'd need nearly a billion petabytes to store the result, and we'd need centuries to compute it. The way around these problems is to use [modular exponentiation](https://en.wikipedia.org/wiki/Modular_exponentiation) where we apply the modulus to each intermediate result, and cut the exponent in half each iteration, so we need only do *O*(log *n*) multiplications, not *O*(*n*). That's a big difference: 10<sup>24</sup> is a trillion trillion, and log<sub>2</sub>(10<sup>24</sup>) is only 80. \n",
+    "Just one more thing: none of this would work unless we can efficiently compute *a*<sup>(*n* - 1)</sup> (mod *n*).  How does the `pow` builtin function do it? When *a* and *n* are 24-digit numbers, if we naively tried to compute `a ** (n - 1)` and then apply (mod *n*), we'd have two problems: we'd need nearly a billion petabytes to store the result, and we'd need centuries to compute it. The way around these problems is to use [modular exponentiation](https://en.wikipedia.org/wiki/Modular_exponentiation) where we apply the modulus to each intermediate result, and cut the exponent in half each iteration, so we need only do *O*(log *n*) multiplications, not *O*(*n*). That's a big difference: 10<sup>24</sup> is a trillion trillion, and log<sub>2</sub>(10<sup>24</sup>) is only 80. \n",
     "\n",
     "There are two key ides that make this work:\n",
     "1) *b*<sup>2*e*</sup> = (*b* × *b*)<sup>*e*</sup>\n",

py/pytudes.py

@@ -23,8 +23,8 @@ notebooks = {
  'How many electoral votes would Trump get if he wins the state where he has positive net approval?')],
  
 'Advent of Code': [
-('Advent of Code 2025: AI LLM Edition', 2024, 'Advent-2025-AI.ipynb', 'Using large language coding models to solve AoC puzzles'),
-('Advent of Code 2025', 2024, 'Advent-2025.ipynb', 'Puzzle site with a coding puzzle for 12 days of Christmas, December 2025'),
+('Advent of Code 2025: AI LLM Edition', 2025, 'Advent-2025-AI.ipynb', 'Using large language coding models to solve AoC puzzles'),
+('Advent of Code 2025', 2025, 'Advent-2025.ipynb', 'Puzzle site with a coding puzzle for 12 days of Christmas, December 2025'),
 ('Advent of Code 2024', 2024, 'Advent-2024.ipynb', 'Puzzle site with a coding puzzle each day of Advent, December 2024'),
 ('Advent of Code 2023', 2023, 'Advent-2023.ipynb', 'Puzzle site with a coding puzzle each day of Advent, December 2023'),
 ('Advent of Code 2022', 2022, 'Advent-2022.ipynb', 'Puzzle site with a coding puzzle each day of Advent, December 2022'),
@@ -98,7 +98,7 @@ notebooks = {
 ('Lottery', 2019, 'RiddlerLottery.ipynb',  'Can you find what lottery number tickets these five friends picked?'),
 ('How Many Soldiers to Beat the Night King?', 2019, 'NightKing.ipynb',  'A battle between the army of the dead and the army of the living'),
 ('Misanthropic Neighbors', 2017, 'Mean%20Misanthrope%20Density.ipynb', 'How crowded will this neighborhood be, if nobody wants to live next door to anyone else?'),
-('Properly Ordered Card Hands', 2018, 'Orderable%20Cards.ipynb', 'Can you get your hand of cards into a nice order with just one move?'),
+('Properly Organized Card Hands', 2018, 'Orderable%20Cards.ipynb', 'Can you get your hand of cards into a nice order with just one move?'),
 ('Race Track', 2021, 'RaceTrack.ipynb', 'Race virtual cars around a circular track defined on a grid of points.'),
 ('Split the States', 2021, 'SplitStates.ipynb', 'Split the US states into two near-halves by area.'),
 ('Tour de 538', 2020, 'TourDe538.ipynb', 'Solve a puzzle involving the best pace for a bicycle race.'),
@@ -143,6 +143,7 @@ import re
 import urllib.request
 
 current_year = 2026
+new_year     = current_year - 2 # What `find_newest` looks for
 
 def read_url(url: str) -> str:
     """Reads a file from the specified URL and returns its content as a string."""
@@ -178,7 +179,7 @@ def format_notebooks() -> str:
     find_newest(notebooks)
     return '\n'.join(format_category(name) for name in notebooks)
 
-def find_newest(notebooks, label='New', year=current_year-1) -> None:
+def find_newest(notebooks, label='New', year=new_year) -> None:
     """Mutate `notebooks['New']` to have a collection of newest notebooks."""
     for category in notebooks:
         for line in notebooks[category]:
@@ -220,7 +221,7 @@ def format_python(url, description, doc='') -> str:
 
 body = f"""
 <div align="right" style="text-align:right"><i>Peter Norvig
-<br><a href="https://github.com/norvig/pytudes/blob/main/LICENSE">MIT License</a><br>2015-2022</i></div>
+<br><a href="https://github.com/norvig/pytudes/blob/main/LICENSE">MIT License</a><br>2015-2026</i></div>
 
 # pytudes
 
@@ -233,7 +234,6 @@ This project contains ***pytudes***—Python programs, usually short, for perfec
 
 To continue the musical analogy, some people think of programming like [Spotify](http://spotify.com): they want to know how to install the app, find a good playlist, and hit the "play" button; after that they don't want to think about it. There are plenty of other tutorials that will tell you how to do the equivalent of that for various programming tasks—this one won't help. But if you think of programming like playing the piano—a craft that can take [years](https://norvig.com/21-days.html) to perfect—then I hope this collection can help.
 
-
 # Index of Jupyter (IPython) Notebooks
 
 For each notebook you can hover on the title to see a description, or click the title to view on github, or click one of the letters in the left column to launch the notebook on 
@@ -250,15 +250,30 @@ For each notebook you can hover on the title to see a description, or click the
 {format_pythons()}
 
 # Etudes for Programmers
+
 I got the idea for the *"etudes"* part of the name from
 this [1978 book](https://books.google.com/books/about/Etudes_for_programmers.html?id=u89WAAAAMAAJ)
 by [Charles Wetherell](http://demin.ws/blog/english/2012/08/25/interview-with-charles-wetherell)
-that was very influential to me when I was first learning to program. I still have my copy.
+that was very influential to me when I was first learning to program. I still have my copy, but
+it is now easier to find a [pdf](txt/Etudes.pdf) than a hard copy.
 
 ![](https://images-na.ssl-images-amazon.com/images/I/51ZnZH29dvL._SX394_BO1,204,203,200_.jpg)
+
+# Reviews of pytudes
+
+Here's what some people are saying about `pytudes`:
+- "What I find interesting is how Peter builds bottom-up solutions using low-level utilities... Reading his code is educational." - [Jeremey Howard](https://en.wikipedia.org/wiki/Jeremy_Howard_(entrepreneur)), co-founder of fast.ai and chief scientist at Kaggle
+- "Everything I see from Peter Norvig is just always so incredibly well written and coded." — [Jonathan](https://news.ycombinator.com/user?id=jypepin), [Hacker News](https://news.ycombinator.com/item?id=27379366)
+- "Peter Norvig is my go to recommendation when someone is interested in becoming better at solving day to day problems ... I feel his skill of dividing a problem into small pieces and expressing them in code in a natural way is unparalleled." — [mikevin](https://news.ycombinator.com/user?id=mikevin), [Hacker News](https://news.ycombinator.com/item?id=27379366)
+- "I've never seen Peter Norvig choose anything but the most elegant and perfect data model for the problem at hand." — [spoonjim](https://news.ycombinator.com/user?id=spoonjim), [Hacker News](https://news.ycombinator.com/item?id=27379366)
+- "I just find Norvig's style of "functional Python" lovely in its own way (with noted disregard of Pep8 and other "best practices")" —[raverbashing](https://news.ycombinator.com/user?id=raverbashing), [Hacker News](https://news.ycombinator.com/item?id=25654955)
+- "You should check out Norvig's design of computer programs [course on Udacity](https://imp.i115008.net/c/2331964/788805/11298?u=https://www.udacity.com/course/design-of-computer-programs--cs212) where he uses these kinds of puzzle programs to teach programming design concepts. It is a hard but really rewarding course. — [nafizh](https://news.ycombinator.com/user?id=nafizh), [HN ACademy](https://yahnd.com/academy/r/udacity.com/course/design-of-computer-programs--cs212/)
+- "Often enough I would think of something [a possible improvement[, but if you worked it out in detail there was some less-obvious reason the code was the way it was... All the code is pretty short, and it's not really 'production code', but it's enough to be an education in craftsmanship at every level."
+- [What code samples should programmers read?] "Anything else implemented by Norvig, he's one of the best programmers that I've had the pleasure of reading code from." - [jacquesm](https://news.ycombinator.com/user?id=jacquesm) on [Hacker News](https://news.ycombinator.com/item?id=14487724)
+- "Everything I see from Peter Norvig is just always so incredibly well written and coded. Every year looking at his solutions for advent of code [0] brings just so much learnings. Strongly recommend. - [jyepin](https://news.ycombinator.com/user?id=jypepin) [Hacker News](https://news.ycombinator.com/item?id=27379366)
+- "I feel his skill of dividing a problem into small pieces and expressing them in code in a natural way is unparalleled." - [mikevin](https://news.ycombinator.com/user?id=mikevin) [Hacker News](https://news.ycombinator.com/item?id=27379366)
 """
 
-output = 'README.md'
-print(f'Wrote {open(output, "w").write(body)} characters to {output}')
-print('Checking...')
-check()
+with open('README.md', "w") as out:
+    print(f'Wrote {out.write(body)} characters to {out.name}')
+    #print('Checking...'); check()