Refactor questions about solutions in Sicherman Dice

Rephrase questions regarding solutions for composite and perfect square numbers.

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

@@ -5,24 +5,19 @@ on:
     paths:
       - 'py/pytudes.py'
 
-env:
-  FORCE_JAVASCRIPT_ACTIONS_TO_NODE24: "true"
-
 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
+        uses: actions/checkout@v7
 
       - name: Set up Python
-        uses: actions/setup-python@v4
+        uses: actions/setup-python@v7
-        with:
-          python-version: '3.10'
 
       - name: Run pytudes.py
         run: python py/pytudes.py
@@ -32,6 +27,5 @@ jobs:
           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

@@ -34,7 +34,6 @@ For each notebook you can hover on the title to see a description, or click the
 | [co](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/TruncatablePrimes.ipynb) [nb](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/TruncatablePrimes.ipynb) | 2026 | <a href="ipynb/TruncatablePrimes.ipynb" title="Prime numbers where you can remove digits and still get primes.">Truncatable Primes</a> |
 | [co](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Advent-2025.ipynb) [nb](https://nbviewer.jupyter.org/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> |
 | [co](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Advent-2025-AI.ipynb) [nb](https://nbviewer.jupyter.org/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> |
-| [co](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Advent-2025-AI.ipynb) [nb](https://nbviewer.jupyter.org/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> |
 
 
 |Open|Year|Large Language Models|
@@ -114,7 +113,7 @@ For each notebook you can hover on the title to see a description, or click the
 | [co](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Stubborn.ipynb) [nb](https://nbviewer.jupyter.org/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> |
 | [co](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/SquareSum.ipynb) [nb](https://nbviewer.jupyter.org/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 Chain Puzzle</a> |
 | [co](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Cheryl.ipynb) [nb](https://nbviewer.jupyter.org/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> |
-| [co](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Cheryl-and-Eve.ipynb) [nb](https://nbviewer.jupyter.org/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> |
+| [co](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Cheryl-and-Eve.ipynb) [nb](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Cheryl-and-Eve.ipynb) | 2015 | <a href="ipynb/Cheryl-and-Eve.ipynb" title="Inventing  puzzles in the Style of Cheryl's Birthday">When Cheryl Met Eve: A Birthday Story</a> |
 | [co](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/xkcd1313.ipynb) [nb](https://nbviewer.jupyter.org/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> |
 | [co](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/xkcd1313-part2.ipynb) [nb](https://nbviewer.jupyter.org/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> |
 

ipynb/Golomb-Puzzle.ipynb

@@ -61,7 +61,7 @@
     "> 9 × 7 × 5 × 3 × 1 = 945.\n",
     "\n",
     "(It is always a relief when two methods give the same answer.)\n",
-    "          \n",
+    "\n",
     "**Method 3: Write a program to enumerate the sets:** We'll represent the 1 × 3 rectangle as the tuple `(1, 3)` and the example set of rectangles as the set\n",
     "\n",
     "    {(1, 3), (2, 4), (5, 7), (6, 8), (9, 10)}\n",

ipynb/Sicherman Dice.ipynb

@@ -487,7 +487,7 @@
    "source": [
     "**Bo: Look at that!**\n",
     "\n",
-    "Ali: It turns out you can <a href=\"https://www.mathartfun.com/dSpecial.html\">buy</a> a pair of dice with just these numbers, and there are some nice [charts and tables on Wikipedia](https://en.wikipedia.org/wiki/Sicherman_dice) explaining it all.  \n",
+    "Ali: It turns out you can <a href=\"https://www.mathartfun.com/dSpecial.html\">buy</a> a pair of dice with just these numbers, and there are some nice [charts and tables on Wikipedia](https://en.wikipedia.org/wiki/Sicherman_dice) ing it all.  \n",
     "\n",
     "![Sicherman dice from MathArtFun.com](http://www.mathartfun.com/shopsite_sc/store/html/SichermanDots.jpg)\n",
     "\n",
@@ -1317,7 +1317,7 @@
     "\n",
     "Ali: In general, what's the sum of the sides of a standard pair?\n",
     "\n",
-    "**Bo: Easy, that's *N* × (*N* + 1). [Gauss](http://betterexplained.com/articles/techniques-for-adding-the-numbers-1-to-100/) knew that when he was in elementary school!**\n",
+    "**Bo: Easy, that's *N* × (*N* + 1). [Gauss](http://bettered.com/articles/techniques-for-adding-the-numbers-1-to-100/) knew that when he was in elementary school!**\n",
     "\n",
     "# Better Efficiency\n",
     "\n",
@@ -1727,11 +1727,11 @@
     "|3|0| | |\n",
     "|4 | 1 | [1, 2, 2, 3]                 |            [1, 3, 3, 5]|\n",
     "|5|0| | |\n",
-    "|6 | 1 | [1, 2, 2, 3, 3, 4]            |           [1, 3, 4, 5, 6, 8]\n",
+    "|6 | 1 | [1, 2, 2, 3, 3, 4]            |           [1, 3, 4, 5, 6, 8]|\n",
-    "|7 | 0 |\n",
+    "|7 | 0 | | |\n",
     "|8 | 3 | [1, 2, 2, 3, 3, 4, 4, 5]         |        [1, 3, 5, 5, 7, 7, 9, 11]|\n",
-    " |||          [1, 2, 3, 3, 4, 4, 5, 6]         |        [1, 2, 5, 5, 6, 6, 9, 10]|\n",
+    "|||          [1, 2, 3, 3, 4, 4, 5, 6]         |        [1, 2, 5, 5, 6, 6, 9, 10]|\n",
-    " |||          [1, 2, 2, 3, 5, 6, 6, 7]        |         [1, 3, 3, 5, 5, 7, 7, 9]|\n",
+    "|||          [1, 2, 2, 3, 5, 6, 6, 7]        |         [1, 3, 3, 5, 5, 7, 7, 9]|\n",
     "|     9  |1 | [1, 2, 2, 3, 3, 3, 4, 4, 5]        |      [1, 4, 4, 7, 7, 7, 10, 10, 13]|\n",
     "|    10 | 1 | [1, 2, 2, 3, 3, 4, 4, 5, 5, 6]      |     [1, 3, 5, 6, 7, 8, 9, 10, 12, 14]|\n",
     "|    11  |0|||\n",
@@ -1751,10 +1751,9 @@
     "\n",
     "- Do all composite *N* have solutions?\n",
     "- Does any prime *N* have a solution?\n",
-    "- Do some *N* have more than the 3 solutions that 8 has?\n",
     "- Does the fact that 8 has 3 solutions have anything to do with the fact that 8 is a perfect cube?\n",
     "- What about the 7 solutions for 12? 12 has 6 factors; does that matter?\n",
-    "- The 9 perfect squares, 4 and 9, have 1 solution each; is that true of all perfect squares?\n",
+    "- The perfect squares 4 and 9 have 1 solution each; is that true of all perfect squares?\n",
     "- Could we make this 10 times faster? 100 times?\n",
     "- Could we handle greater values of *N* if we worked with [generating functions](https://en.wikipedia.org/wiki/Sicherman_dice)?\n",
     "- What about Sicherman triples (3 nonstandard dice with the same distribution of sums as 3 standard dice)?\n",

py/pytudes.py

@@ -75,7 +75,7 @@ notebooks = {
 ("Stubborn number endings", 2024, 'Stubborn.ipynb', 'Any number ending in 5 has a square that also ends in 5. What other endings are like this?'), 
 ('Square Sum Chain Puzzle', 2020, 'SquareSum.ipynb', 'Place the numbers from 1 to n in a chain (or a circle) such that adjacent pairs sum to a perfect square'),
 ("When is Cheryl's Birthday?", 2020, 'Cheryl.ipynb', "Solving the *Cheryl's Birthday* logic puzzle"),
-('When Cheryl Met Eve: A Birthday Story', 2015, 'Cheryl-and-Eve.ipynb', "Inventing new puzzles in the Style of Cheryl's Birthday"),
+('When Cheryl Met Eve: A Birthday Story', 2015, 'Cheryl-and-Eve.ipynb', "Inventing  puzzles in the Style of Cheryl's Birthday"),
 ('xkcd 1313: Regex Golf', 2015, 'xkcd1313.ipynb', 'Find the smallest regular expression; inspired by Randall Munroe'),
 ('xkcd 1313: Regex Golf (Part 2: Infinite Problems)', 2015, 'xkcd1313-part2.ipynb', 'Regex Golf: better, faster, funner (with Stefan Pochmann)')],
 
@@ -194,13 +194,13 @@ def format_notebooks() -> str:
     find_newest(notebooks)
     return '\n'.join(format_category(name) for name in notebooks)
 
-def find_newest(notebooks, label='New', year=new_year) -> None:
+def find_newest(notebooks, New='New', year=new_year) -> None:
-    """Mutate `notebooks['New']` to have a collection of newest notebooks."""
+    """Mutate `notebooks[New]` to have a collection of newest notebooks, from `new_year` or later."""
     for category in notebooks:
         for line in notebooks[category]:
-            if line[1] >= year:
+            if line[1] >= year and line not in notebooks[New]:
-                notebooks[label].append(line)
+                notebooks[New].append(line)
-    notebooks[label].sort(key=lambda line: (-line[1], line[0]))
+    notebooks[New].sort(key=lambda line: (-line[1], line[0]))
     
 def format_category(category) -> str:
     """Make a table of multiple jupyter/ipython notebooks, under a header."""