From d74e7cbcec2d47a89386cc627c91c11179526d85 Mon Sep 17 00:00:00 2001
From: Peter Norvig <peter.norvig@gmail.com>
Date: Sat, 28 Dec 2024 00:20:07 -0800
Subject: [PATCH] Add files via upload

---
 ipynb/Advent-2024.ipynb | 7020 ++++++++++++++++-----------------------
 ipynb/AdventUtils.ipynb |   85 +-
 2 files changed, 2997 insertions(+), 4108 deletions(-)

diff --git a/ipynb/Advent-2024.ipynb b/ipynb/Advent-2024.ipynb
index 7d1b63e..382b036 100644
--- a/ipynb/Advent-2024.ipynb
+++ b/ipynb/Advent-2024.ipynb
@@ -18,7 +18,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 668,
+   "execution_count": 2,
    "id": "ed82ed5b-a42d-468b-8f6e-288d3c2de20b",
    "metadata": {},
    "outputs": [
@@ -64,7 +64,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 671,
+   "execution_count": 5,
    "id": "22e5d621-a152-4712-866f-f8b962b5dd14",
    "metadata": {},
    "outputs": [
@@ -117,7 +117,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 673,
+   "execution_count": 7,
    "id": "8d6bc9f5-5fa1-4dad-bd43-d957833d8ea9",
    "metadata": {},
    "outputs": [],
@@ -129,7 +129,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 674,
+   "execution_count": 8,
    "id": "6ada5e5b-2fb7-4198-a5bb-7b2af4b9270a",
    "metadata": {},
    "outputs": [
@@ -139,7 +139,7 @@
        "Puzzle  1.1:   .000 seconds, answer 1830467           ok"
       ]
      },
-     "execution_count": 674,
+     "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -161,7 +161,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 676,
+   "execution_count": 10,
    "id": "0131e096-38d1-4c13-9e9c-b0d09839a5cf",
    "metadata": {},
    "outputs": [],
@@ -174,7 +174,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 677,
+   "execution_count": 11,
    "id": "6f6c298a-53a1-4d80-8747-7dd713d4d4f0",
    "metadata": {},
    "outputs": [
@@ -184,7 +184,7 @@
        "Puzzle  1.2:   .000 seconds, answer 26674158          ok"
       ]
      },
-     "execution_count": 677,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -206,7 +206,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 679,
+   "execution_count": 13,
    "id": "10e1ab83-a6ec-4143-ad9a-eaae220adcde",
    "metadata": {},
    "outputs": [
@@ -257,7 +257,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 681,
+   "execution_count": 15,
    "id": "0f6b6744-e93d-47cf-accd-daab9f3650d0",
    "metadata": {},
    "outputs": [],
@@ -282,7 +282,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 683,
+   "execution_count": 17,
    "id": "c0cc052b-e9ef-4757-a860-4cd34dd00fb8",
    "metadata": {},
    "outputs": [],
@@ -301,7 +301,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 685,
+   "execution_count": 19,
    "id": "e662bf10-4d6a-40f1-95ce-dfc39f5b3fc2",
    "metadata": {},
    "outputs": [
@@ -311,7 +311,7 @@
        "Puzzle  2.1:   .000 seconds, answer 257               ok"
       ]
      },
-     "execution_count": 685,
+     "execution_count": 19,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -335,7 +335,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 687,
+   "execution_count": 21,
    "id": "67ba1d53-95b7-4811-b225-2ff15d6bdc5c",
    "metadata": {},
    "outputs": [],
@@ -353,7 +353,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 688,
+   "execution_count": 22,
    "id": "d1b9ffb5-af7a-465f-a063-c31df2d0605c",
    "metadata": {},
    "outputs": [
@@ -363,7 +363,7 @@
        "Puzzle  2.2:   .002 seconds, answer 328               ok"
       ]
      },
-     "execution_count": 688,
+     "execution_count": 22,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -385,7 +385,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 690,
+   "execution_count": 24,
    "id": "78080200-0f9f-4492-9bee-c936737ee96f",
    "metadata": {},
    "outputs": [
@@ -424,7 +424,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1119,
+   "execution_count": 26,
    "id": "bf6366b1-6952-47d8-8b3c-09f8d05ec093",
    "metadata": {},
    "outputs": [],
@@ -438,17 +438,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1121,
+   "execution_count": 27,
    "id": "2032c903-5f23-4c16-ba68-410b6c1750e1",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle  3.1:   .002 seconds, answer 156388521         ok"
+       "Puzzle  3.1:   .001 seconds, answer 156388521         ok"
       ]
      },
-     "execution_count": 1121,
+     "execution_count": 27,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -468,7 +468,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1124,
+   "execution_count": 29,
    "id": "85844f51-1396-4299-ba5b-c61064ee02b6",
    "metadata": {},
    "outputs": [],
@@ -488,7 +488,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 697,
+   "execution_count": 31,
    "id": "4525d01a-bac0-41c2-92b8-baf0fd395e88",
    "metadata": {},
    "outputs": [],
@@ -500,7 +500,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 698,
+   "execution_count": 32,
    "id": "ce40f258-ca76-48c3-9965-27a6979a4243",
    "metadata": {},
    "outputs": [
@@ -510,7 +510,7 @@
        "Puzzle  3.2:   .000 seconds, answer 75920122          ok"
       ]
      },
-     "execution_count": 698,
+     "execution_count": 32,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -532,7 +532,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 700,
+   "execution_count": 34,
    "id": "a0d903b9-018e-4861-9314-cafed59055fd",
    "metadata": {},
    "outputs": [
@@ -566,12 +566,12 @@
    "source": [
     "### Part 1: How many times does XMAS appear?\n",
     "\n",
-    "We just have to find how many times the word \"XMAS\" appears in the grid, horizontally, vertically, or diagonally, forwards or backwards.  The variable `directions8` contains those eight directions (as (delta-x, delta-y) pairs). So examine each square of the grid and if it contains \"X\", see in how many of the directions it spells \"XMAS\". (Note that locations in the grid are denoted by `(x, y)` coordinates, as are directions (e.g., `(1, 0)` is the `East` direction. The functions `add2` and `mul2` do addition and scalar multiplication on these 2D vectors.)"
+    "We just have to find how many times the word \"XMAS\" appears in the grid, horizontally, vertically, or diagonally, forwards or backwards.  The variable `directions8` contains those eight directions (as (delta-x, delta-y) pairs). So examine each square of the grid and if it contains \"X\", see in how many of the directions it spells \"XMAS\". (Note that locations in the grid are denoted by `(x, y)` coordinates, as are directions (e.g., `(1, 0)` is the `East` direction. (The functions `add` and `mul` do addition and scalar multiplication on these 2D vectors.)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 702,
+   "execution_count": 36,
    "id": "72d48abb-7a82-452f-b91d-838b3836a90f",
    "metadata": {},
    "outputs": [],
@@ -585,23 +585,23 @@
     "\n",
     "def grid_can_spell(grid, start, dir, word):\n",
     "    \"\"\"Does `word` appear in grid starting at `start` and going in direction `dir`?\"\"\"\n",
-    "    return all(grid[add2(start, mul2(dir, i))] == word[i] \n",
+    "    return all(grid[add(start, mul(dir, i))] == word[i] \n",
     "               for i in range(len(word)))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 703,
+   "execution_count": 37,
    "id": "6175362b-d8b4-45d1-b70c-d8575a0fe188",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle  4.1:   .022 seconds, answer 2401              ok"
+       "Puzzle  4.1:   .020 seconds, answer 2401              ok"
       ]
      },
-     "execution_count": 703,
+     "execution_count": 37,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -629,7 +629,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 705,
+   "execution_count": 39,
    "id": "3d8a051f-cf7b-4e8c-b0fb-78c3f089989d",
    "metadata": {},
    "outputs": [],
@@ -639,15 +639,15 @@
     "def x_search(grid: Grid, word='MAS') -> int:\n",
     "    \"\"\"How many times does an X-MAS appear in the grid?\"\"\"\n",
     "    A = word[1] # The letter in the middle of the cross\n",
-    "    return quantify((grid_can_spell(grid, sub2(mid_pos, dir1), dir1, word) and\n",
-    "                     grid_can_spell(grid, sub2(mid_pos, dir2), dir2, word))\n",
+    "    return quantify((grid_can_spell(grid, sub(mid_pos, dir1), dir1, word) and\n",
+    "                     grid_can_spell(grid, sub(mid_pos, dir2), dir2, word))\n",
     "                    for mid_pos in grid.findall(A) # All positions where A appears\n",
     "                    for dir1, dir2 in diagonal_pairs)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 706,
+   "execution_count": 40,
    "id": "64cde1d9-f58c-4633-b5da-87908a02f76d",
    "metadata": {},
    "outputs": [
@@ -657,7 +657,7 @@
        "Puzzle  4.2:   .016 seconds, answer 1822              ok"
       ]
      },
-     "execution_count": 706,
+     "execution_count": 40,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -683,7 +683,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 708,
+   "execution_count": 42,
    "id": "b77a5a1f-a43b-4ce8-a60c-94d69a595505",
    "metadata": {},
    "outputs": [
@@ -746,7 +746,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 710,
+   "execution_count": 44,
    "id": "4c85a23e-686a-4129-a14c-ff6f6a88b9ac",
    "metadata": {},
    "outputs": [],
@@ -767,7 +767,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 712,
+   "execution_count": 46,
    "id": "78898d37-46ff-4367-9d89-b2a107a90aa1",
    "metadata": {},
    "outputs": [],
@@ -785,7 +785,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 713,
+   "execution_count": 47,
    "id": "b1c87359-1d2d-4a90-8305-9d152ce5d547",
    "metadata": {},
    "outputs": [
@@ -795,7 +795,7 @@
        "Puzzle  5.1:   .001 seconds, answer 5762              ok"
       ]
      },
-     "execution_count": 713,
+     "execution_count": 47,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -818,7 +818,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 715,
+   "execution_count": 49,
    "id": "d8718c3e-0b3b-49ce-8cca-abd82aa788d7",
    "metadata": {},
    "outputs": [
@@ -828,7 +828,7 @@
        "23"
       ]
      },
-     "execution_count": 715,
+     "execution_count": 49,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -850,7 +850,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1135,
+   "execution_count": 51,
    "id": "7222dc1c-067f-4bb5-84e1-3c2fc72fd53a",
    "metadata": {},
    "outputs": [],
@@ -867,17 +867,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1137,
+   "execution_count": 52,
    "id": "494cda6e-6b07-4054-9b03-45f61bd4f973",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle  5.2:   .003 seconds, answer 4130              ok"
+       "Puzzle  5.2:   .001 seconds, answer 4130              ok"
       ]
      },
-     "execution_count": 1137,
+     "execution_count": 52,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -907,7 +907,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 721,
+   "execution_count": 55,
    "id": "6ec71cf8-c43d-457e-8e14-0e9eb99b956a",
    "metadata": {},
    "outputs": [
@@ -950,7 +950,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1146,
+   "execution_count": 57,
    "id": "95f0b409-a6d6-47bc-8ce5-1c2df80f2b18",
    "metadata": {},
    "outputs": [],
@@ -959,7 +959,7 @@
     "    \"\"\"A list of all points in the path followed by the guard.\n",
     "    The guard turns right when there is an obstacle ahead, otherwise goes forward.\"\"\"\n",
     "    path = grid.findall(guard) # A one-element list of positions, e.g. [(3, 4)]\n",
-    "    while (ahead := add2(path[-1], facing)) in grid:\n",
+    "    while (ahead := add(path[-1], facing)) in grid:\n",
     "        if grid[ahead] == '#':\n",
     "            facing = make_turn(facing, 'R')\n",
     "        else:\n",
@@ -969,17 +969,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 724,
+   "execution_count": 58,
    "id": "f4be3d1f-7f24-4d55-8221-df0026178e1e",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle  6.1:   .002 seconds, answer 5329              ok"
+       "Puzzle  6.1:   .001 seconds, answer 5329              ok"
       ]
      },
-     "execution_count": 724,
+     "execution_count": 58,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1010,7 +1010,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 726,
+   "execution_count": 60,
    "id": "1718fecb-aa3e-4162-9948-1c06d4ec5e8a",
    "metadata": {},
    "outputs": [],
@@ -1018,7 +1018,7 @@
     "def is_loopy_path(grid: Grid, guard_pos, facing=North) -> bool:\n",
     "    \"\"\"Does the path followed by the guard form a loop?\"\"\"\n",
     "    path = {(guard_pos, facing)}\n",
-    "    while (ahead := add2(guard_pos, facing)) in grid:\n",
+    "    while (ahead := add(guard_pos, facing)) in grid:\n",
     "        if grid[ahead] == '#':\n",
     "            facing = make_turn(facing, 'R')\n",
     "            if (guard_pos, facing) in path:\n",
@@ -1040,17 +1040,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 727,
+   "execution_count": 61,
    "id": "36196264-eb33-4fc0-95d5-06c985105ebf",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle  6.2:  1.976 seconds, answer 2162              ok"
+       "Puzzle  6.2:  1.998 seconds, answer 2162              ok"
       ]
      },
-     "execution_count": 727,
+     "execution_count": 61,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1082,7 +1082,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 730,
+   "execution_count": 64,
    "id": "c1c6cee8-122c-43c9-8c7d-ed8980ea2b76",
    "metadata": {},
    "outputs": [
@@ -1143,7 +1143,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 733,
+   "execution_count": 67,
    "id": "6fa3907c-0e1a-4d4a-9fc3-f809b9325674",
    "metadata": {},
    "outputs": [
@@ -1153,7 +1153,7 @@
        "13"
       ]
      },
-     "execution_count": 733,
+     "execution_count": 67,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1174,7 +1174,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1207,
+   "execution_count": 69,
    "id": "5dfe0edf-cf29-4623-bb2c-6180f832f4d7",
    "metadata": {},
    "outputs": [],
@@ -1192,17 +1192,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1209,
+   "execution_count": 70,
    "id": "3085596d-f5ec-4ba8-b05a-cf70cf276a0c",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle  7.1:   .026 seconds, answer 1985268524462     ok"
+       "Puzzle  7.1:   .014 seconds, answer 1985268524462     ok"
       ]
      },
-     "execution_count": 1209,
+     "execution_count": 70,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1224,7 +1224,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1219,
+   "execution_count": 72,
    "id": "393a50cf-f136-446a-a97e-c501669ce89f",
    "metadata": {},
    "outputs": [],
@@ -1234,17 +1234,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1221,
+   "execution_count": 73,
    "id": "f8e75ea3-e8ba-4b33-8efe-8bf74357e35d",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle  7.2:   .807 seconds, answer 150077710195188   ok"
+       "Puzzle  7.2:   .803 seconds, answer 150077710195188   ok"
       ]
      },
-     "execution_count": 1221,
+     "execution_count": 73,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1264,7 +1264,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1223,
+   "execution_count": 75,
    "id": "6fe6adad-a3a6-49b8-b49e-6098b27e3a44",
    "metadata": {},
    "outputs": [],
@@ -1285,17 +1285,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1225,
+   "execution_count": 76,
    "id": "ffb673f1-af9d-4d15-8f8d-92e29489dd78",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle  7.2:   .616 seconds, answer 150077710195188   ok"
+       "Puzzle  7.2:   .606 seconds, answer 150077710195188   ok"
       ]
      },
-     "execution_count": 1225,
+     "execution_count": 76,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1305,6 +1305,24 @@
     "       sum(numbers[0] for numbers in equations if can_be_calibrated(numbers, operators3)))"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "ecb4bdf5-89ef-4625-8d7b-acbaeb86a18a",
+   "metadata": {},
+   "source": [
+    "Now that we're done with the first week, I'm going to clean up by deleting some of the big data structures that are hanging around."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 78,
+   "id": "ed4d4095-d417-4328-9c22-42c22606c482",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "reports = xmas_grid = manual = rules = updates = lab_grid = equations = None"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "2e5693b7-dab8-4f89-a000-c69ee75a11c9",
@@ -1317,7 +1335,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 744,
+   "execution_count": 80,
    "id": "cf6361a7-e3bc-42ec-ae16-f9eec166055e",
    "metadata": {},
    "outputs": [
@@ -1358,7 +1376,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1229,
+   "execution_count": 82,
    "id": "22180ce8-5d03-4aee-8c73-62f2afbddf71",
    "metadata": {},
    "outputs": [],
@@ -1379,17 +1397,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1231,
+   "execution_count": 83,
    "id": "dd173ce9-cbbb-4282-b43f-c7cff662bd90",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle  8.1:   .004 seconds, answer 220               ok"
+       "Puzzle  8.1:   .003 seconds, answer 220               ok"
       ]
      },
-     "execution_count": 1231,
+     "execution_count": 83,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1413,7 +1431,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1237,
+   "execution_count": 85,
    "id": "d30f8ce9-f186-46a0-a2e7-f74eceae6905",
    "metadata": {},
    "outputs": [],
@@ -1433,17 +1451,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1239,
+   "execution_count": 86,
    "id": "6bf85b57-8b8f-4196-9903-6d5fe082f404",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle  8.1:   .004 seconds, answer 220               ok"
+       "Puzzle  8.1:   .002 seconds, answer 220               ok"
       ]
      },
-     "execution_count": 1239,
+     "execution_count": 86,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1455,17 +1473,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1241,
+   "execution_count": 87,
    "id": "f232952c-5fc6-4696-a8b1-d0b54137ac02",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle  8.2:   .006 seconds, answer 813               ok"
+       "Puzzle  8.2:   .003 seconds, answer 813               ok"
       ]
      },
-     "execution_count": 1241,
+     "execution_count": 87,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1495,7 +1513,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 754,
+   "execution_count": 90,
    "id": "0e944f9e-5c16-440c-b12e-178058a87048",
    "metadata": {},
    "outputs": [
@@ -1548,7 +1566,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1273,
+   "execution_count": 92,
    "id": "76e8454d-a2f3-4b6b-92df-182116cf46e0",
    "metadata": {},
    "outputs": [],
@@ -1580,17 +1598,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1275,
+   "execution_count": 93,
    "id": "2aa7e2b9-844e-49ed-b41b-4a4cecff86b7",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle  9.1:   .036 seconds, answer 6332189866718     ok"
+       "Puzzle  9.1:   .020 seconds, answer 6332189866718     ok"
       ]
      },
-     "execution_count": 1275,
+     "execution_count": 93,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1618,7 +1636,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1277,
+   "execution_count": 95,
    "id": "fcf4d832-3d7d-4987-aa57-e6e0f1df16bf",
    "metadata": {},
    "outputs": [],
@@ -1660,17 +1678,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1279,
+   "execution_count": 96,
    "id": "e3036875-88d0-496e-9d2f-facd0e80a5b2",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle  9.2:  2.424 seconds, answer 6353648390778     ok"
+       "Puzzle  9.2:  2.428 seconds, answer 6353648390778     ok"
       ]
      },
-     "execution_count": 1279,
+     "execution_count": 96,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1700,7 +1718,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1283,
+   "execution_count": 99,
    "id": "5804fb03-05f3-402f-b6cc-6804c5d22512",
    "metadata": {},
    "outputs": [
@@ -1753,7 +1771,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 765,
+   "execution_count": 101,
    "id": "76b5379e-ee19-4607-91b8-88ec7b38023f",
    "metadata": {},
    "outputs": [],
@@ -1769,7 +1787,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 766,
+   "execution_count": 102,
    "id": "97cf05f7-fa56-4a90-b2d8-2cd4d9b81f95",
    "metadata": {},
    "outputs": [
@@ -1779,7 +1797,7 @@
        "Puzzle 10.1:   .005 seconds, answer 744               ok"
       ]
      },
-     "execution_count": 766,
+     "execution_count": 102,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1803,7 +1821,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 768,
+   "execution_count": 104,
    "id": "b763450f-a565-4936-bee4-e531c2eeebdb",
    "metadata": {},
    "outputs": [],
@@ -1829,17 +1847,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1294,
+   "execution_count": 106,
    "id": "f8a87032-6556-4fc9-9bb8-573611aee8dc",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle 10.2:   .014 seconds, answer 1651              ok"
+       "Puzzle 10.2:   .006 seconds, answer 1651              ok"
       ]
      },
-     "execution_count": 1294,
+     "execution_count": 106,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1861,10 +1879,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1309,
+   "execution_count": 108,
    "id": "eea7e277-4687-48a9-85b5-a031a9d4b6e1",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "def plot_topo(topo: Grid):\n",
     "    \"\"\"Show the map with a colormap from blue to red.\"\"\"\n",
@@ -1890,7 +1919,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1292,
+   "execution_count": 110,
    "id": "76b68cef-d8de-4145-b65c-b254fedf1671",
    "metadata": {},
    "outputs": [
@@ -1934,7 +1963,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 775,
+   "execution_count": 112,
    "id": "1513df56-3d6f-42cf-8aec-1bdbeb991d90",
    "metadata": {},
    "outputs": [],
@@ -1960,17 +1989,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 776,
+   "execution_count": 113,
    "id": "eff17cd0-a2c7-4d69-bc55-c0ef97917915",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle 11.1:   .062 seconds, answer 194482            ok"
+       "Puzzle 11.1:   .066 seconds, answer 194482            ok"
       ]
      },
-     "execution_count": 776,
+     "execution_count": 113,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1996,7 +2025,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 778,
+   "execution_count": 115,
    "id": "707b5a97-0296-48df-bdab-e34064cc67c2",
    "metadata": {},
    "outputs": [],
@@ -2021,17 +2050,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 780,
+   "execution_count": 117,
    "id": "efdcdbf8-e8ec-4a85-9d09-90a20e08c66a",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle 11.1:   .002 seconds, answer 194482            ok"
+       "Puzzle 11.1:   .001 seconds, answer 194482            ok"
       ]
      },
-     "execution_count": 780,
+     "execution_count": 117,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2043,17 +2072,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 781,
+   "execution_count": 118,
    "id": "657b1f13-ffcc-44c6-84f1-398fa2fcdac7",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle 11.2:   .055 seconds, answer 232454623677743   ok"
+       "Puzzle 11.2:   .061 seconds, answer 232454623677743   ok"
       ]
      },
-     "execution_count": 781,
+     "execution_count": 118,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2085,7 +2114,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 784,
+   "execution_count": 121,
    "id": "8161ee7e-76e3-499a-abf8-a607991c9602",
    "metadata": {},
    "outputs": [
@@ -2124,7 +2153,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1316,
+   "execution_count": 123,
    "id": "79f91f38-e325-44f2-9e53-b64ce12d9d35",
    "metadata": {},
    "outputs": [],
@@ -2141,7 +2170,7 @@
     "def perimeter_length(region: Region) -> int:\n",
     "    \"\"\"The number of sides on the perimeter of the region: \n",
     "    ones where the adjacent position in some direction is not in the region.\"\"\"\n",
-    "    return quantify(add2(plot, d) not in region \n",
+    "    return quantify(add(plot, d) not in region \n",
     "                    for plot in region for d in directions4)"
    ]
   },
@@ -2155,7 +2184,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1319,
+   "execution_count": 125,
    "id": "1fbabbfb-50c8-4197-8517-e7cee9582765",
    "metadata": {},
    "outputs": [],
@@ -2179,17 +2208,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1321,
+   "execution_count": 126,
    "id": "cdaf655b-d12c-4973-b19b-3132e5e691c6",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle 12.1:   .053 seconds, answer 1402544           ok"
+       "Puzzle 12.1:   .033 seconds, answer 1402544           ok"
       ]
      },
-     "execution_count": 1321,
+     "execution_count": 126,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2229,7 +2258,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1323,
+   "execution_count": 128,
    "id": "38c30e15-3a33-40c2-b734-163a15af7a8a",
    "metadata": {},
    "outputs": [],
@@ -2242,8 +2271,8 @@
     "    \n",
     "def region_sides(region):\n",
     "    \"\"\"How many straight-line sides does this region have?\"\"\"\n",
-    "    def has_edge(p: Point, d: Vector): return p in region and add2(p, d) not in region\n",
-    "    def neighbor(p: Point, d: Vector): return add2(p, make_turn(d, 'R'))\n",
+    "    def has_edge(p: Point, d: Vector): return p in region and add(p, d) not in region\n",
+    "    def neighbor(p: Point, d: Vector): return add(p, make_turn(d, 'R'))\n",
     "    subtract = quantify(has_edge(p, d) and has_edge(neighbor(p, d), d)\n",
     "                        for p in region\n",
     "                        for d in directions4)\n",
@@ -2252,17 +2281,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1325,
+   "execution_count": 129,
    "id": "72175812-dcd0-4f1b-9efa-0dceeeafa609",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle 12.1:   .054 seconds, answer 1402544           ok"
+       "Puzzle 12.1:   .030 seconds, answer 1402544           ok"
       ]
      },
-     "execution_count": 1325,
+     "execution_count": 129,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2274,17 +2303,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1327,
+   "execution_count": 130,
    "id": "9defcd35-91bc-41d4-a16f-bb7a4ede75e7",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle 12.2:   .069 seconds, answer 862486            ok"
+       "Puzzle 12.2:   .061 seconds, answer 862486            ok"
       ]
      },
-     "execution_count": 1327,
+     "execution_count": 130,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2308,7 +2337,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 795,
+   "execution_count": 132,
    "id": "e78f45c0-c420-4661-aad2-14e122b4473b",
    "metadata": {},
    "outputs": [
@@ -2362,7 +2391,7 @@
     "### Part 1: What is the fewest tokens you would have to spend to win all possible prizes?\n",
     "\n",
     "We are told that for some machines it is possible to reach the prize and others it is impossible. We are also told that you need to spend 3 tokens to  press  the **A** button and 1 token to press the **B** button. There is a hint that no button will need to be pushed more than 100 times. It is usually a good idea to accept the hint, so I will  do the following:\n",
-    "- Exhaustively try from every number from 0 to 100 presses of the **A** button.\n",
+    "- Exhaustively try every number from 0 to 100 presses of the **A** button.\n",
     "- For each number, figure out what the resulting position of the claw would be after those presses.\n",
     "- Calculate how many presses of the **B** button would be required to get to the prize's X location.\n",
     "- If the number of presses is an integer, and would also arrive at the prize's Y location, then yield that solution.\n",
@@ -2372,7 +2401,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 797,
+   "execution_count": 134,
    "id": "c2c4bbc9-42cd-483d-8da2-97cf051e93fe",
    "metadata": {},
    "outputs": [],
@@ -2384,7 +2413,7 @@
     "        pos = mul(A, Apresses)\n",
     "        if X_(pos) > X_(Prize) or Y_(pos) > Y_(Prize):\n",
     "            return\n",
-    "        diff = sub2(Prize, pos)\n",
+    "        diff = sub(Prize, pos)\n",
     "        Bpresses = X_(diff) / X_(B)\n",
     "        if Bpresses.is_integer() and Bpresses * Y_(B) == Y_(diff):\n",
     "            yield (Apresses, int(Bpresses))\n",
@@ -2396,17 +2425,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 798,
+   "execution_count": 135,
    "id": "f5638ed4-1e59-4b9f-b1fc-427d2eb0d036",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle 13.1:   .010 seconds, answer 29598             ok"
+       "Puzzle 13.1:   .006 seconds, answer 29598             ok"
       ]
      },
-     "execution_count": 798,
+     "execution_count": 135,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2421,29 +2450,29 @@
    "id": "3a36e76c-dd5b-4d80-ae88-9980e7d274ac",
    "metadata": {},
    "source": [
-    "### Part 2: What is the fewest tokens you would have to spend to win all possible prizes, now?\n",
+    "### Part 2: Using the corrected prize coordinates, what is the fewest tokens you would have to spend to win all possible prizes?\n",
     "\n",
-    "In Part 2, we discover that the prize is actually much farther away, by 10,000,000,000,000 (ten trillion) steps in both the X and Y coordinates. Theoretically, we could still use `solve_claw` with a bigger `limit`, but that would take a *long* time.\n",
-    "\n",
-    "Instead I can solve each claw machine *mathematically* rather than by trial and error. I know that an equation over the integers is called a [Diophantine equation](https://en.wikipedia.org/wiki/Diophantine_equation), but I don't remember much about them.  What are the equations of a claw machine? For my first machine, \n",
+    "In Part 2, we discover that \"due to a unit conversion error\" the prize is actually much farther away, by 10,000,000,000,000 (ten trillion) steps in both the X and Y coordinates. Theoretically, we could still use `solve_claw` with a bigger `limit`, but that would take a *long* time.\n",
+    "w\n",
+    "Instead I can solve each claw machine *mathematically* rather than by trial and error. It looks like each claw machine defines two equations;  what exactly are the equations? For my first claw machine, \n",
     "\n",
     "     Button A: X+24, Y+19\n",
     "     Button B: X+32, Y+86\n",
     "     Prize: X=1072, Y=2062\n",
     "\n",
-    "there are two linear equations to solve simultaneously:\n",
+    "there are two linear equations to solve simultaneously, over the integers:\n",
     "\n",
     "     24 A + 32 B = 1072\n",
     "     19 A + 86 B = 2062\n",
     "\n",
-    "In general, two linear equations in two unknowns can have zero solutions (if the lines are parallel), an infinite number of solutions (if the lines are the same), or exactly one solution (otherwise). The further constraint that *A* and *B* have to be non-negative integers may rule out some of these solutions, but mostly we are looking for the one point where two lines intersect.\n",
+    "I know that an equation over the integers is called a [Diophantine equation](https://en.wikipedia.org/wiki/Diophantine_equation), but I don't remember much about them, and furthermore it seems like it is more important that we are dealing with lines than that they need integer solutions. In general, two linear equations in two unknowns can have zero solutions (if the lines are parallel), an infinite number of solutions (if the lines are the same), or exactly one solution (in the \"normal\" case). We can solve the linear equations, and then discard the answer if *A* and *B* are not integers. \n",
     "\n",
     "I defined `solve_claw` to yield multiple solutions, but let's see how many solutions each claw machine yields:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 800,
+   "execution_count": 137,
    "id": "df8da2ae-52f9-409b-a54f-ad7d21b32e45",
    "metadata": {},
    "outputs": [
@@ -2453,7 +2482,7 @@
        "Counter({0: 168, 1: 152})"
       ]
      },
-     "execution_count": 800,
+     "execution_count": 137,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2469,7 +2498,7 @@
    "source": [
     "This says that 168 claw machines have no solution and 152 have exactly one. None of them have more than one solution.\n",
     "\n",
-    "So, what is the intersection point of two lines? You could [look it up](https://www.wolframalpha.com/input?i=solve+for+a%2C+b%3A+p+*+a+%2B+q+*+b+%3D+r++and+++s+*+a+%2B+t+*+b+%3D+u) or work it out by hand, or [call a function](https://numpy.org/doc/2.1/reference/generated/numpy.linalg.solve.html). Given the two equations over the two variables *a* and *b*:\n",
+    "So, what is the intersection point of two lines? You could [look it up](https://www.wolframalpha.com/input?i=solve+for+a%2C+b%3A+p+*+a+%2B+q+*+b+%3D+r++and+++s+*+a+%2B+t+*+b+%3D+u) or work it out by hand, or [call a library function](https://numpy.org/doc/2.1/reference/generated/numpy.linalg.solve.html). Given the two equations over the variables *a* and *b*:\n",
     "\n",
     "    p * a + q * b = r\n",
     "    s * a + t * b = u\n",
@@ -2484,7 +2513,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 802,
+   "execution_count": 139,
    "id": "6bbd0934-d962-4c93-940b-810651e9e568",
    "metadata": {},
    "outputs": [],
@@ -2494,7 +2523,7 @@
     "    ((p, s), (q, t), (r, u)) = claw\n",
     "    a = (r * t - q * u) / (p * t - q * s)\n",
     "    b = (r * s - p * u) / (q * s - p * t)\n",
-    "    if a >= 0 and b >= 0 and a.is_integer() and b.is_integer():\n",
+    "    if a.is_integer() and b.is_integer():\n",
     "        yield (int(a), int(b))"
    ]
   },
@@ -2503,24 +2532,26 @@
    "id": "af52d98e-50e9-4c4d-875f-1ed2b3dc8111",
    "metadata": {},
    "source": [
-    "We'll need a function to move the claws further away, then we're ready to answer Part 2:"
+    "This raises an interesting design point: If you have a function that might return zero or one result of type `T`, should you define the return type as `Optional[T]` or as `Iterable[T]`, where it can yield zero or one result? I guess it depends on the expected use cases of the function.\n",
+    "\n",
+    "We'll need a way to move the prizes further away, then we're ready to answer Part 2:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 804,
+   "execution_count": 141,
    "id": "dd38ba4c-44ba-426b-b1c8-0e10adbdd642",
    "metadata": {},
    "outputs": [],
    "source": [
-    "def move_prize(claw, delta=(10**13, 10**13)) -> Claw:\n",
-    "    \"\"\"Move the claw's prize by the given displacement, delta.\"\"\"\n",
-    "    return claw._replace(Prize=(add(claw.Prize, delta)))"
+    "def move_prizes(claws, delta=(10**13, 10**13)) -> List[Claw]:\n",
+    "    \"\"\"Move each claw's prize by the given displacement, delta.\"\"\"\n",
+    "    return [claw._replace(Prize=(add(claw.Prize, delta))) for claw in claws]"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 805,
+   "execution_count": 142,
    "id": "9f578b3e-6b6d-4eb0-9228-c98122a84747",
    "metadata": {},
    "outputs": [
@@ -2530,14 +2561,14 @@
        "Puzzle 13.2:   .000 seconds, answer 93217456941970    ok"
       ]
      },
-     "execution_count": 805,
+     "execution_count": 142,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "answer(13.2, 93217456941970, lambda:\n",
-    "       sum(cheapest_solution(move_prize(claw)) for claw in claws))"
+    "       sum(map(cheapest_solution, move_prizes(claws))))"
    ]
   },
   {
@@ -2550,7 +2581,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 807,
+   "execution_count": 144,
    "id": "609ed4ce-548c-4af4-8e09-c621aca0124e",
    "metadata": {},
    "outputs": [
@@ -2560,7 +2591,7 @@
        "Puzzle 13.1:   .000 seconds, answer 29598             ok"
       ]
      },
-     "execution_count": 807,
+     "execution_count": 144,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2575,7 +2606,7 @@
    "id": "741bd221-cda4-432b-8ad2-b8c6950c7dc3",
    "metadata": {},
    "source": [
-    "I could have recognized in Part 1 that we have a system of two linear equations in two unknowns, and gone straight to the Part 2 solution. But I have no regrets; I took the hint that trial-and-test for 100 trials was a good idea, and I saved the complicated algebra for when I really needed it in Part 2. Having two independent implementations give the answer incrreases my confidence in both of them."
+    "I could have recognized in Part 1 that we have a system of two linear equations in two unknowns, and implemented the Part 2 solution. But I have no regrets; I took the hint that trial-and-test for 100 trials was a good idea, and I saved the complicated algebra for when I really needed it in Part 2. Having two independent implementations that produce the same answer increases my confidence in both of them."
    ]
   },
   {
@@ -2590,7 +2621,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 810,
+   "execution_count": 147,
    "id": "1a5f5875-426d-47ea-a35a-405c39ced5dd",
    "metadata": {},
    "outputs": [
@@ -2626,7 +2657,7 @@
     }
    ],
    "source": [
-    "robots = parse(14, ints)"
+    "robots = parse(14, ints) "
    ]
   },
   {
@@ -2636,12 +2667,14 @@
    "source": [
     "### Part 1: What will the safety factor be after exactly 100 seconds have elapsed?\n",
     "\n",
-    "Each second the  robots move according to their velocity, and they wrap around when they reach the edge of their world, which has width 101 and height 103. They can pass through each other. We're asked to figure out where they are after 100 seconds. I can see that it is not necessary to step the robots each time step; we can just multiply their velocity by time, add it to their initial position, and then take the result modulo the width or height. That's done in `robot_dance`. We're asked to figure out how many robots end up in each **quadrant**. There are four quadrants, but a robot that is exactly on a middle line, either horizontally or vertically, doesn't count). Finally, the **safety factor** is the product of the count of robots in each quadrant."
+    "Each second the  robots move according to their velocity, and they wrap around when they reach the edge of their world, which has width 101 and height 103. They never collide; they can pass right through each other. We're asked to figure out where they are after 100 seconds. I can see that it is not necessary to simulate the robots movements time step by time step; we can just multiply their velocity by time, add it to their initial position, and then take the result modulo the width or height. That's done in `robot_dance`. \n",
+    "\n",
+    "We're asked to figure out how many robots end up in each **quadrant**. There are four quadrants, but a robot that is exactly on a middle line, either horizontally or vertically, doesn't count in any quadrant. Finally, the **safety factor** is the product of the four counts of robots in each quadrant."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 812,
+   "execution_count": 149,
    "id": "be22ac94-7401-4cf6-ab83-e43775536af7",
    "metadata": {},
    "outputs": [],
@@ -2657,13 +2690,13 @@
     "                   for (x, y) in positions if x != w and y != h)\n",
     "\n",
     "def safety_factor(robots) -> int:\n",
-    "    \"\"\"The product of the counts in each of the four quadrants.\"\"\"\n",
+    "    \"\"\"The product of the four counts of robots in each quadrant.\"\"\"\n",
     "    return prod(quadrant_counts(robot_dance(robots)).values())"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 813,
+   "execution_count": 150,
    "id": "69093001-79aa-463a-b801-51cd5b4de4eb",
    "metadata": {},
    "outputs": [
@@ -2673,7 +2706,7 @@
        "Puzzle 14.1:   .000 seconds, answer 216027840         ok"
       ]
      },
-     "execution_count": 813,
+     "execution_count": 150,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2683,6 +2716,35 @@
     "       safety_factor(robots))"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "06b4e335-9863-40f7-983a-0744884dbc20",
+   "metadata": {},
+   "source": [
+    "In case you're curious, here are the quadrant counts after 100 steps:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 152,
+   "id": "08661dc5-445c-4908-b0b4-57f3a53e5179",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Counter({(1, 1): 124, (-1, 1): 122, (-1, -1): 120, (1, -1): 119})"
+      ]
+     },
+     "execution_count": 152,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "quadrant_counts(robot_dance(robots))"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "a0cb27ad-82ff-4dcb-85cf-596b16ae9875",
@@ -2690,19 +2752,19 @@
    "source": [
     "### Part 2: What is the fewest number of seconds that must elapse for the robots to display a picture of a Christmas Tree?\n",
     "\n",
-    "I was so sure Part 2 was going to ask for 10 trillion steps. But I was wrong. \n",
+    "I was **so** sure that Part 2 was going to ask for 10 trillion steps, and I was going to be **so** clever for not simulating step-by-step. But I was wrong. \n",
     "\n",
-    "Instead they ask the very vague question of when a picture emerges. They gave the hint that \"*very rarely, most of the robots should arrange themselves into a picture of a Christmas tree.*\" Since I don't know exactly how to specify a Christmas tree picture, I see three options:\n",
-    "- I could build an animation, and watch as each frame is displayed, stopping when I see something that looks like a tree.\n",
-    "- The phrase \"*most of the robots should arrange themselves*\" suggests that most of the robots are in one area. I could check for that.\n",
-    "- Generate an image for each time step and send it off to an image recognition service. That would be iffy, and possibly expensive. \n",
+    "Instead we have the very vague task of discovering when a picture emerges. There is a hint that \"*very rarely, most of the robots should arrange themselves into a picture of a Christmas tree.*\" Since I don't know exactly how to specify a picture of a Christmas tree, I see three options:\n",
+    "1) I could build an animation, and watch as each frame is displayed, stopping when I see something that looks like a tree.\n",
+    "2) The phrase \"*most of the robots should arrange themselves*\" suggests that most of the robots are in one area. I could check for that.\n",
+    "3) I could generate an image for each time step and send it off to an AI image recognition service. That would be iffy, slow, and probably expensive. \n",
     "\n",
     "I'll try the animation approach first. Google and Stack Overflow led me to the `matplotlib.animation.FuncAnimation` function:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 815,
+   "execution_count": 154,
    "id": "664c686e-0c3d-43b8-970f-88c0bf47dbf6",
    "metadata": {},
    "outputs": [],
@@ -2712,7 +2774,7 @@
     "def animate_robots(robots, times: Ints):\n",
     "    \"\"\"Animate the robot dance over the given time steps.\"\"\"\n",
     "    plt.rcParams[\"animation.html\"] = \"jshtml\"\n",
-    "    plt.rcParams['figure.dpi'] = 150  \n",
+    "    plt.rcParams['figure.dpi'] = 100  \n",
     "    plt.ioff()\n",
     "    fig, ax = plt.subplots()\n",
     "    def animate(t: int):\n",
@@ -2734,7 +2796,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 817,
+   "execution_count": 156,
    "id": "87843969-cb37-4fa5-9788-6a1b71c43521",
    "metadata": {},
    "outputs": [
@@ -2926,42 +2988,42 @@
        "</style>\n",
        "\n",
        "<div class=\"animation\">\n",
-       "  <img id=\"_anim_img371f62c512dc43638cafc61e9bb8bb48\">\n",
+       "  <img id=\"_anim_img6bb1e1ef68eb46a0ba61a1ed392b533e\">\n",
        "  <div class=\"anim-controls\">\n",
-       "    <input id=\"_anim_slider371f62c512dc43638cafc61e9bb8bb48\" type=\"range\" class=\"anim-slider\"\n",
+       "    <input id=\"_anim_slider6bb1e1ef68eb46a0ba61a1ed392b533e\" type=\"range\" class=\"anim-slider\"\n",
        "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
-       "           oninput=\"anim371f62c512dc43638cafc61e9bb8bb48.set_frame(parseInt(this.value));\">\n",
+       "           oninput=\"anim6bb1e1ef68eb46a0ba61a1ed392b533e.set_frame(parseInt(this.value));\">\n",
        "    <div class=\"anim-buttons\">\n",
-       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anim371f62c512dc43638cafc61e9bb8bb48.slower()\">\n",
+       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anim6bb1e1ef68eb46a0ba61a1ed392b533e.slower()\">\n",
        "          <i class=\"fa fa-minus\"></i></button>\n",
-       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anim371f62c512dc43638cafc61e9bb8bb48.first_frame()\">\n",
+       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anim6bb1e1ef68eb46a0ba61a1ed392b533e.first_frame()\">\n",
        "        <i class=\"fa fa-fast-backward\"></i></button>\n",
-       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anim371f62c512dc43638cafc61e9bb8bb48.previous_frame()\">\n",
+       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anim6bb1e1ef68eb46a0ba61a1ed392b533e.previous_frame()\">\n",
        "          <i class=\"fa fa-step-backward\"></i></button>\n",
-       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anim371f62c512dc43638cafc61e9bb8bb48.reverse_animation()\">\n",
+       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anim6bb1e1ef68eb46a0ba61a1ed392b533e.reverse_animation()\">\n",
        "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
-       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anim371f62c512dc43638cafc61e9bb8bb48.pause_animation()\">\n",
+       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anim6bb1e1ef68eb46a0ba61a1ed392b533e.pause_animation()\">\n",
        "          <i class=\"fa fa-pause\"></i></button>\n",
-       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anim371f62c512dc43638cafc61e9bb8bb48.play_animation()\">\n",
+       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anim6bb1e1ef68eb46a0ba61a1ed392b533e.play_animation()\">\n",
        "          <i class=\"fa fa-play\"></i></button>\n",
-       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anim371f62c512dc43638cafc61e9bb8bb48.next_frame()\">\n",
+       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anim6bb1e1ef68eb46a0ba61a1ed392b533e.next_frame()\">\n",
        "          <i class=\"fa fa-step-forward\"></i></button>\n",
-       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anim371f62c512dc43638cafc61e9bb8bb48.last_frame()\">\n",
+       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anim6bb1e1ef68eb46a0ba61a1ed392b533e.last_frame()\">\n",
        "          <i class=\"fa fa-fast-forward\"></i></button>\n",
-       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anim371f62c512dc43638cafc61e9bb8bb48.faster()\">\n",
+       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anim6bb1e1ef68eb46a0ba61a1ed392b533e.faster()\">\n",
        "          <i class=\"fa fa-plus\"></i></button>\n",
        "    </div>\n",
-       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select371f62c512dc43638cafc61e9bb8bb48\"\n",
+       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select6bb1e1ef68eb46a0ba61a1ed392b533e\"\n",
        "          class=\"anim-state\">\n",
-       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_371f62c512dc43638cafc61e9bb8bb48\"\n",
+       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_6bb1e1ef68eb46a0ba61a1ed392b533e\"\n",
        "             >\n",
-       "      <label for=\"_anim_radio1_371f62c512dc43638cafc61e9bb8bb48\">Once</label>\n",
-       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_371f62c512dc43638cafc61e9bb8bb48\"\n",
+       "      <label for=\"_anim_radio1_6bb1e1ef68eb46a0ba61a1ed392b533e\">Once</label>\n",
+       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_6bb1e1ef68eb46a0ba61a1ed392b533e\"\n",
        "             checked>\n",
-       "      <label for=\"_anim_radio2_371f62c512dc43638cafc61e9bb8bb48\">Loop</label>\n",
-       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_371f62c512dc43638cafc61e9bb8bb48\"\n",
+       "      <label for=\"_anim_radio2_6bb1e1ef68eb46a0ba61a1ed392b533e\">Loop</label>\n",
+       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_6bb1e1ef68eb46a0ba61a1ed392b533e\"\n",
        "             >\n",
-       "      <label for=\"_anim_radio3_371f62c512dc43638cafc61e9bb8bb48\">Reflect</label>\n",
+       "      <label for=\"_anim_radio3_6bb1e1ef68eb46a0ba61a1ed392b533e\">Reflect</label>\n",
        "    </form>\n",
        "  </div>\n",
        "</div>\n",
@@ -2971,2863 +3033,1756 @@
        "  /* Instantiate the Animation class. */\n",
        "  /* The IDs given should match those used in the template above. */\n",
        "  (function() {\n",
-       "    var img_id = \"_anim_img371f62c512dc43638cafc61e9bb8bb48\";\n",
-       "    var slider_id = \"_anim_slider371f62c512dc43638cafc61e9bb8bb48\";\n",
-       "    var loop_select_id = \"_anim_loop_select371f62c512dc43638cafc61e9bb8bb48\";\n",
+       "    var img_id = \"_anim_img6bb1e1ef68eb46a0ba61a1ed392b533e\";\n",
+       "    var slider_id = \"_anim_slider6bb1e1ef68eb46a0ba61a1ed392b533e\";\n",
+       "    var loop_select_id = \"_anim_loop_select6bb1e1ef68eb46a0ba61a1ed392b533e\";\n",
        "    var frames = new Array(3);\n",
        "    \n",
-       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA8AAAALQCAYAAABfdxm0AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
-       "bGliIHZlcnNpb24zLjkuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8hTgPZAAAACXBIWXMAABcS\\\n",
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-       "tmvdEtMGt7tbBHcfGyGf7ypt/GC7yGbXz6eOMSSr3W27te1WtoUShKBV6BZC6k/UGqLDj4xKJBAY\\\n",
-       "IJD5/sFOSMj8uPfMufeec+7r+Xj4eLRk7tz3Pfecc+/JzH0lEI/H4yAiIiIiIiIyXI7XBRARERER\\\n",
-       "ERG5gQtgIiIiIiIi8gUugImIiIiIiMgXuAAmIiIiIiIiX+ACmIiIiIiIiHyBC2AiIiIiIiLyBS6A\\\n",
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+       "/Hn3SAghhBBC/IAxgIQQQgghIYMbQEIIIYSQkMENICGEEEJIyOAGkBBCCCEkZHADSAghhBASMrgB\\\n",
+       "JIQQQggJGdwAEkIIIYSEDG4ACSGEEEJCBjeAhBBCCCEhgxtAQgghhJCQwQ0gIYQQQkjI4AaQEEII\\\n",
+       "ISRkcANICCGEEBIyuAEkhBBCCAkZ3AASQgghhIQMbgAJIYQQQkIGN4CEEEIIISGDG0BCCCGEkJDB\\\n",
+       "DSAhhBBCSMjgBpAQQgghJGRwA0gIIYQQEjK4ASSEEEIICRncABJCCCGEhAxuAAkhhBBCQgY3gIQQ\\\n",
+       "QgghIYMbQEIIIYSQkMENICGEEEJIyOAGkBBCCCEkZHADSAghhBASMrgBJIQQQggJGdwAEkIIIYSE\\\n",
+       "jP8PE1yu61RT0JYAAAAASUVORK5CYII=\\\n",
        "\"\n",
        "\n",
        "\n",
        "    /* set a timeout to make sure all the above elements are created before\n",
        "       the object is initialized. */\n",
        "    setTimeout(function() {\n",
-       "        anim371f62c512dc43638cafc61e9bb8bb48 = new Animation(frames, img_id, slider_id, 200.0,\n",
+       "        anim6bb1e1ef68eb46a0ba61a1ed392b533e = new Animation(frames, img_id, slider_id, 200.0,\n",
        "                                 loop_select_id);\n",
        "    }, 0);\n",
        "  })()\n",
        "</script>\n"
       ],
       "text/plain": [
-       "<matplotlib.animation.FuncAnimation at 0x15c8178c0>"
+       "<matplotlib.animation.FuncAnimation at 0x1326aba10>"
       ]
      },
-     "execution_count": 817,
+     "execution_count": 156,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5848,7 +4803,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 819,
+   "execution_count": 158,
    "id": "9563d49c-54a3-439f-a833-f48c2a070609",
    "metadata": {},
    "outputs": [],
@@ -5865,7 +4820,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 820,
+   "execution_count": 159,
    "id": "ab8c7e3b-f400-4976-ad0d-5f92cbadec02",
    "metadata": {},
    "outputs": [
@@ -6057,42 +5012,42 @@
        "</style>\n",
        "\n",
        "<div class=\"animation\">\n",
-       "  <img id=\"_anim_imged69eeb3dff848aba82de90936e3b8cc\">\n",
+       "  <img id=\"_anim_imgc44333b0e24f41239f8df1807c200349\">\n",
        "  <div class=\"anim-controls\">\n",
-       "    <input id=\"_anim_slidered69eeb3dff848aba82de90936e3b8cc\" type=\"range\" class=\"anim-slider\"\n",
+       "    <input id=\"_anim_sliderc44333b0e24f41239f8df1807c200349\" type=\"range\" class=\"anim-slider\"\n",
        "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
-       "           oninput=\"animed69eeb3dff848aba82de90936e3b8cc.set_frame(parseInt(this.value));\">\n",
+       "           oninput=\"animc44333b0e24f41239f8df1807c200349.set_frame(parseInt(this.value));\">\n",
        "    <div class=\"anim-buttons\">\n",
-       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"animed69eeb3dff848aba82de90936e3b8cc.slower()\">\n",
+       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"animc44333b0e24f41239f8df1807c200349.slower()\">\n",
        "          <i class=\"fa fa-minus\"></i></button>\n",
-       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"animed69eeb3dff848aba82de90936e3b8cc.first_frame()\">\n",
+       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"animc44333b0e24f41239f8df1807c200349.first_frame()\">\n",
        "        <i class=\"fa fa-fast-backward\"></i></button>\n",
-       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"animed69eeb3dff848aba82de90936e3b8cc.previous_frame()\">\n",
+       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"animc44333b0e24f41239f8df1807c200349.previous_frame()\">\n",
        "          <i class=\"fa fa-step-backward\"></i></button>\n",
-       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"animed69eeb3dff848aba82de90936e3b8cc.reverse_animation()\">\n",
+       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"animc44333b0e24f41239f8df1807c200349.reverse_animation()\">\n",
        "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
-       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"animed69eeb3dff848aba82de90936e3b8cc.pause_animation()\">\n",
+       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"animc44333b0e24f41239f8df1807c200349.pause_animation()\">\n",
        "          <i class=\"fa fa-pause\"></i></button>\n",
-       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"animed69eeb3dff848aba82de90936e3b8cc.play_animation()\">\n",
+       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"animc44333b0e24f41239f8df1807c200349.play_animation()\">\n",
        "          <i class=\"fa fa-play\"></i></button>\n",
-       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"animed69eeb3dff848aba82de90936e3b8cc.next_frame()\">\n",
+       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"animc44333b0e24f41239f8df1807c200349.next_frame()\">\n",
        "          <i class=\"fa fa-step-forward\"></i></button>\n",
-       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"animed69eeb3dff848aba82de90936e3b8cc.last_frame()\">\n",
+       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"animc44333b0e24f41239f8df1807c200349.last_frame()\">\n",
        "          <i class=\"fa fa-fast-forward\"></i></button>\n",
-       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"animed69eeb3dff848aba82de90936e3b8cc.faster()\">\n",
+       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"animc44333b0e24f41239f8df1807c200349.faster()\">\n",
        "          <i class=\"fa fa-plus\"></i></button>\n",
        "    </div>\n",
-       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_selected69eeb3dff848aba82de90936e3b8cc\"\n",
+       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_selectc44333b0e24f41239f8df1807c200349\"\n",
        "          class=\"anim-state\">\n",
-       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_ed69eeb3dff848aba82de90936e3b8cc\"\n",
+       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_c44333b0e24f41239f8df1807c200349\"\n",
        "             >\n",
-       "      <label for=\"_anim_radio1_ed69eeb3dff848aba82de90936e3b8cc\">Once</label>\n",
-       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_ed69eeb3dff848aba82de90936e3b8cc\"\n",
+       "      <label for=\"_anim_radio1_c44333b0e24f41239f8df1807c200349\">Once</label>\n",
+       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_c44333b0e24f41239f8df1807c200349\"\n",
        "             checked>\n",
-       "      <label for=\"_anim_radio2_ed69eeb3dff848aba82de90936e3b8cc\">Loop</label>\n",
-       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_ed69eeb3dff848aba82de90936e3b8cc\"\n",
+       "      <label for=\"_anim_radio2_c44333b0e24f41239f8df1807c200349\">Loop</label>\n",
+       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_c44333b0e24f41239f8df1807c200349\"\n",
        "             >\n",
-       "      <label for=\"_anim_radio3_ed69eeb3dff848aba82de90936e3b8cc\">Reflect</label>\n",
+       "      <label for=\"_anim_radio3_c44333b0e24f41239f8df1807c200349\">Reflect</label>\n",
        "    </form>\n",
        "  </div>\n",
        "</div>\n",
@@ -6102,723 +5057,408 @@
        "  /* Instantiate the Animation class. */\n",
        "  /* The IDs given should match those used in the template above. */\n",
        "  (function() {\n",
-       "    var img_id = \"_anim_imged69eeb3dff848aba82de90936e3b8cc\";\n",
-       "    var slider_id = \"_anim_slidered69eeb3dff848aba82de90936e3b8cc\";\n",
-       "    var loop_select_id = \"_anim_loop_selected69eeb3dff848aba82de90936e3b8cc\";\n",
+       "    var img_id = \"_anim_imgc44333b0e24f41239f8df1807c200349\";\n",
+       "    var slider_id = \"_anim_sliderc44333b0e24f41239f8df1807c200349\";\n",
+       "    var loop_select_id = \"_anim_loop_selectc44333b0e24f41239f8df1807c200349\";\n",
        "    var frames = new Array(1);\n",
        "    \n",
-       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA8AAAALQCAYAAABfdxm0AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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+       "vdHU1GSmTp1qevfubbp06WL69u1rZsyYYXbv3t16DHWdmWXLlsX9fp4wYYIxJrV63bVrl7noootM\\\n",
+       "jx49TFFRkRkzZoxZt26dD2fjjogxxvgz9ggAAAA/kAMIAAAQMnQAAQAAQoYOIAAAQMjQAQQAAAgZ\\\n",
+       "OoAAAAAhQwcQAAAgZOgAAgAAhAwdQAAAgJChAwgAABAydAABAABChg4gAABAyNABBAAACBk6gAAA\\\n",
+       "ACFDBxAAACBk6AACAACEDB1AAACAkKEDCAAAEDJ0AAEAAEKGDiAAAEDI0AEEAAAIGTqAAAAAIUMH\\\n",
+       "EAAAIGToAAIAAIQMHUAAAICQoQMIAAAQMnQAAQAAQoYOIAAAQMjQAQQAAAgZOoAAAAAhQwcQAAAg\\\n",
+       "ZOgAAgAAhMz/B+2RGq47XolVAAAAAElFTkSuQmCC\\\n",
        "\"\n",
        "\n",
        "\n",
        "    /* set a timeout to make sure all the above elements are created before\n",
        "       the object is initialized. */\n",
        "    setTimeout(function() {\n",
-       "        animed69eeb3dff848aba82de90936e3b8cc = new Animation(frames, img_id, slider_id, 200.0,\n",
+       "        animc44333b0e24f41239f8df1807c200349 = new Animation(frames, img_id, slider_id, 200.0,\n",
        "                                 loop_select_id);\n",
        "    }, 0);\n",
        "  })()\n",
        "</script>\n"
       ],
       "text/plain": [
-       "<matplotlib.animation.FuncAnimation at 0x168352c00>"
+       "<matplotlib.animation.FuncAnimation at 0x132e9ac00>"
       ]
      },
-     "execution_count": 820,
+     "execution_count": 159,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6835,24 +5475,24 @@
    "source": [
     "**It worked!** \n",
     "\n",
-    "(At first I had a **bug**: the Christmas tree was upside down, because the Y-axis was upside down. So I added the `yaxis.set_inverted` call to `animate_robots`.)\n",
+    "(At first I had a **bug**: the Christmas tree was upside down, because my Y-axis was upside down. So I added the `yaxis.set_inverted` call to `animate_robots`.)\n",
     "\n",
     "Although there was a human in the loop to verify the output, I can make this official with this call to `answer`:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 822,
+   "execution_count": 161,
    "id": "75434bc8-35ae-4d8b-b747-01d773472541",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle 14.2:  1.833 seconds, answer 6876              ok"
+       "Puzzle 14.2:  1.874 seconds, answer 6876              ok"
       ]
      },
-     "execution_count": 822,
+     "execution_count": 161,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6869,12 +5509,12 @@
    "source": [
     "# [Day 15](https://adventofcode.com/2024/day/15): Warehouse Woes\n",
     "\n",
-    "Today's input is in two sections: the first section is a grid map describing a warehouse with walls (`#`) and boxes (`O`) and one robot (`@`). The second part is a set of instructions for how the robot moves (arrows). I'll parse the two sections as paragraphs, then parse each paragraph:"
+    "Today's input is in two sections: the first section is a grid map describing a warehouse with walls (`#`) and boxes (`O`) and a single robot (`@`). The second part is a set of instructions for how the robot moves (arrows). I'll parse the two sections as paragraphs, then parse each paragraph:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 824,
+   "execution_count": 163,
    "id": "20be45ec-f6fc-472c-9b49-872b7334528c",
    "metadata": {},
    "outputs": [
@@ -6920,12 +5560,12 @@
     "\n",
     "The **GPS coordinate** of a box at (*x*, *y*) is defined to be *x* + 100*y*.\n",
     "\n",
-    "I'll implement `obey_arrows` to make the arrow moves on a copy of the warehouse. For each arrow it finds all boxes that might move (and the robot) with `moveables`, then `make_movement` checks if they would bump into a wall, and if not, they all move."
+    "I'll implement `obey_arrows` to make the arrow moves on a copy of the warehouse. For each arrow the function finds all the things that might move (the robot and any boxes) with `moveables`; then `make_movement` checks if they would bump into a wall, and if not, they all move."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 826,
+   "execution_count": 165,
    "id": "248d51c0-424e-4bbb-bbf4-37cdc18313e1",
    "metadata": {},
    "outputs": [],
@@ -6940,9 +5580,11 @@
     "        dir = arrow_direction[arrow]\n",
     "        robot_and_boxes = moveables(grid, robot_pos, dir)\n",
     "        if make_movement(grid, robot_and_boxes, dir):\n",
-    "            robot_pos = add2(robot_pos, dir)\n",
+    "            robot_pos = add(robot_pos, dir)\n",
     "    return grid\n",
     "\n",
+    "def all_box_positions(grid) -> List[Point]: return grid.findall('O')\n",
+    "\n",
     "def moveables(grid, start: Point, dir: Vector) -> List[Point]:\n",
     "    \"\"\"The positions of moveable things (the robot and maybe boxes) going in direction `dir` from the `start`.\"\"\"\n",
     "    def moveable(pos): return grid[pos] in ('@', 'O')\n",
@@ -6950,35 +5592,36 @@
     "\n",
     "def make_movement(grid, to_move: List[Point], dir: Vector) -> bool:\n",
     "    \"\"\"Try to move the objects in the `to_move` positions in direction `dir`; return True if they move.\"\"\"\n",
-    "    if grid[add2(to_move[-1], dir)] == '#':\n",
+    "    def destination(p): return add(p, dir) # Where we are trying to move `p` to\n",
+    "    if grid[destination(to_move[-1])] == '#':\n",
     "        return False\n",
     "    else:\n",
-    "        for p in reversed(to_move):\n",
-    "            grid[add2(p, dir)] = grid[p]\n",
+    "        for p in reversed(to_move): # Reverse order so they don't step on each other\n",
+    "            grid[destination(p)] = grid[p]\n",
     "            grid[p] = '.'\n",
     "        return True"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 827,
+   "execution_count": 166,
    "id": "52e93218-6ac2-4cf7-aced-f4f3a3df77b5",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle 15.1:   .025 seconds, answer 1563092           ok"
+       "Puzzle 15.1:   .026 seconds, answer 1563092           ok"
       ]
      },
-     "execution_count": 827,
+     "execution_count": 166,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "answer(15.1, 1563092, lambda:\n",
-    "       sum(map(gps_coordinate, obey_arrows(warehouse, arrows).findall('O'))))"
+    "       sum(map(gps_coordinate, all_box_positions(obey_arrows(warehouse, arrows)))))"
    ]
   },
   {
@@ -6988,7 +5631,7 @@
    "source": [
     "### Part 2: What is the sum of all boxes' final GPS coordinates on the double-wide grid?\n",
     "\n",
-    "In Part 2, there is another warehouse that is similar to the first, but twice as wide. Each position in the original warehouse is replaced by two copies of the contents, except that the robot is replaced by `@.` and a box, `O`, is replaced by `[]`, indicating the two halves of a double-wide box. The rules for movement and pushing are the same, except that when the robot is moving North or South and is pushing a box, that box, since it is two positions wide, can push *two* boxes if they are lined up right. (Presumably, those two boxes could then push three boxes in the next row, and so on, although the puzzle description did not explicitly specify that). Finally, the GPS coordinates are taken for the `[` part of the box. Here's what it looks like before and after the robot moves \"^\":\n",
+    "In Part 2, there is another warehouse that is similar to the first, but twice as wide. Each position in the original warehouse is replaced by *two* copies of the contents, except that the robot is replaced by `@.` and a box, `O`, is replaced by `[]`, indicating the two halves of a double-wide box. The rules for movement and pushing are the same, except that when the robot is moving North or South and is pushing a box, that box, since it is two positions wide, can push *two* boxes if they are lined up right. (Presumably, those two boxes could then push three boxes in the next row, and so on, although the puzzle description did not explicitly specify that). Finally, the GPS coordinates are taken for the `[` part of the box. Here's what it looks like before and after the robot moves \"^\":\n",
     "\n",
     "        ##############        ##############\n",
     "        ##......##..##        ##......##..##\n",
@@ -7008,7 +5651,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 829,
+   "execution_count": 168,
    "id": "2d9afbc1-75b2-479d-81fc-fbab69d25753",
    "metadata": {},
    "outputs": [],
@@ -7021,32 +5664,32 @@
     "\n",
     "def make_movement(grid, to_move: Collection[Point], dir: Vector) -> bool:\n",
     "    \"\"\"Try to move the objects in the `to_move` positions in direction `dir`; return True if they move.\"\"\"\n",
-    "    def go(p): return add2(p, dir)\n",
-    "    if any(grid[go(p)] == '#' for p in to_move):\n",
+    "    def destination(p): return add(p, dir) # Where we are trying to move `p` to\n",
+    "    if any(grid[destination(p)] == '#' for p in to_move):\n",
     "        return False\n",
     "    else:\n",
-    "        updates = {go(p): grid[p] for p in to_move}\n",
+    "        updates = {destination(p): grid[p] for p in to_move}\n",
     "        grid.update({p: '.' for p in to_move})\n",
     "        grid.update(updates)\n",
     "        return True\n",
     "\n",
     "def moveables(grid, start_pos, dir) -> Set[Point]:\n",
     "    \"\"\"The positions of moveable things (robot and maybe boxes) going in direction from the start.\"\"\" \n",
-    "    ahead = add2(start_pos, dir)\n",
+    "    ahead = add(start_pos, dir)\n",
     "    if dir in (East, West) or grid[ahead] == 'O': # Single line push\n",
     "        def moveable(pos): return grid[pos] in ('@', 'O', '[', ']')\n",
     "        return set(takewhile(moveable, grid.follow_line(start_pos, dir)))\n",
     "    else: # Potential non-linear push\n",
     "        results = {start_pos}\n",
     "        if grid[ahead] in ('[', ']'): results |= moveables(grid, ahead, dir) \n",
-    "        if grid[ahead] == '[':        results |= moveables(grid, add2(ahead, East), dir)\n",
-    "        if grid[ahead] == ']':        results |= moveables(grid, add2(ahead, West), dir)\n",
+    "        if grid[ahead] == '[':        results |= moveables(grid, add(ahead, East), dir)\n",
+    "        if grid[ahead] == ']':        results |= moveables(grid, add(ahead, West), dir)\n",
     "        return results"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 830,
+   "execution_count": 169,
    "id": "7af49bbf-dd10-4221-9096-6f548dec44c0",
    "metadata": {},
    "outputs": [
@@ -7056,7 +5699,7 @@
        "Puzzle 15.1:   .029 seconds, answer 1563092           ok"
       ]
      },
-     "execution_count": 830,
+     "execution_count": 169,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7068,7 +5711,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 831,
+   "execution_count": 170,
    "id": "99246602-a51e-41aa-a7e9-7cdbc8d449ca",
    "metadata": {},
    "outputs": [
@@ -7078,7 +5721,7 @@
        "Puzzle 15.2:   .042 seconds, answer 1582688           ok"
       ]
      },
-     "execution_count": 831,
+     "execution_count": 170,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7093,12 +5736,12 @@
    "id": "4361f8c3-1d15-441e-9a41-b1ea20707651",
    "metadata": {},
    "source": [
-    "I had a frustrating time **debugging** this one; this was by far my worst performance of the year. First I had a silly typo in `moveables`; I was able to fix it after looking at the results on the smaller test puzzle:"
+    "I had a frustrating time **debugging** this one; this was by far my worst performance on this year's puizzles so far. First I had a silly typo in `moveables`; I was able to fix it after looking at the results on the smaller test puzzle:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 833,
+   "execution_count": 172,
    "id": "47c99f0f-ab65-4ae1-a308-42668feacdd5",
    "metadata": {},
    "outputs": [
@@ -7136,7 +5779,7 @@
    "id": "30a6d933-8969-427d-b82f-c5fb95d10164",
    "metadata": {},
    "source": [
-    "That's the correct final grid, so I couldn't see what I had done wrong. It turns out that I had the movements correct, but I my **bug** was summing the GPS coordinates of *both* sides of the boxes when I should have been using just the *left* sides. Lesson learned: read the instructions carefully!"
+    "Once I found my first bug and got this correct final grid, I couldn't see what I had done wrong. It turns out that I had all the movements correct, but my **bug** was summing the GPS coordinates of *both* sides of the boxes when I should have been using just the *left* sides. Lesson learned: read the instructions carefully!"
    ]
   },
   {
@@ -7146,12 +5789,12 @@
    "source": [
     "# [Day 16](https://adventofcode.com/2024/day/16): Reindeer Maze\n",
     "\n",
-    "Today's input is yet another 2D grid, this one a maze that reindeer run through:"
+    "Today's input is yet another 2D grid, this one a maze that reindeer race through:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 836,
+   "execution_count": 175,
    "id": "03255fd5-95d9-4a90-b1bb-abdf6bbf1d85",
    "metadata": {},
    "outputs": [
@@ -7196,7 +5839,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 838,
+   "execution_count": 177,
    "id": "e6e4bfba-0170-436a-961b-d4749f2cd66e",
    "metadata": {},
    "outputs": [],
@@ -7213,12 +5856,12 @@
     "    \"\"\"A GridProblem where a turn costs 1000 points, a step ahead 1.\"\"\"\n",
     "    \n",
     "    def actions(self, state):\n",
-    "        ahead = add2(state.pos, state.facing)\n",
+    "        ahead = add(state.pos, state.facing)\n",
     "        return ['L', 'R'] + ([ahead] if self.grid[ahead] != '#' else [])\n",
     "                \n",
     "    def result(self, state, action) -> State:\n",
     "        return (State(state.pos, make_turn(state.facing, action))   if action in ('L', 'R') else\n",
-    "                State(add2(state.pos, state.facing), state.facing))\n",
+    "                State(add(state.pos, state.facing), state.facing))\n",
     "            \n",
     "    def action_cost(self, s1, action, s2) -> int: return 1000 if action in ('L', 'R') else 1\n",
     "\n",
@@ -7229,17 +5872,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 839,
+   "execution_count": 178,
    "id": "4974c14c-86da-4b86-a55c-6ae8781df207",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle 16.1:   .139 seconds, answer 103512            ok"
+       "Puzzle 16.1:   .146 seconds, answer 103512            ok"
       ]
      },
-     "execution_count": 839,
+     "execution_count": 178,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7261,7 +5904,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 841,
+   "execution_count": 180,
    "id": "692abfea-f9c8-477c-8369-386cdd2a7606",
    "metadata": {},
    "outputs": [],
@@ -7293,17 +5936,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 842,
+   "execution_count": 181,
    "id": "ea9bf9f3-0e6b-4949-a641-6b3db2fd9d32",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle 16.2:   .985 seconds, answer 554               ok"
+       "Puzzle 16.2:   .863 seconds, answer 554               ok"
       ]
      },
-     "execution_count": 842,
+     "execution_count": 181,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7313,6 +5956,24 @@
     "    len(reindeer_best_positions(maze)))"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "479dc79f-44d9-4140-b79d-ebd9132fcfbd",
+   "metadata": {},
+   "source": [
+    "Time to do another cleanup:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 183,
+   "id": "0300f56c-ed13-4d63-a6d1-8c8bcba558ba",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "disk_map = topo = farm = claws = robots = warehouse_woes = warehouse = arrows = maze = None"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "91607c18-56c3-4432-8da8-cfe570887bc0",
@@ -7325,7 +5986,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 844,
+   "execution_count": 185,
    "id": "50fd3cb8-0a6f-4edd-b5cb-f7b1e6f9d987",
    "metadata": {},
    "outputs": [
@@ -7369,7 +6030,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 845,
+   "execution_count": 186,
    "id": "c23b8a44-e352-4a30-abe5-3c939ffc743c",
    "metadata": {},
    "outputs": [
@@ -7379,7 +6040,7 @@
        "Computer(A=52042868, B=0, C=0, prog=[2, 4, 1, 7, 7, 5, 0, 3, 4, 4, 1, 7, 5, 5, 3, 0])"
       ]
      },
-     "execution_count": 845,
+     "execution_count": 186,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7395,12 +6056,12 @@
    "source": [
     "### Part 1: Run the Program. What do you get if you use commas to join the output values?\n",
     "\n",
-    "Now we have to run the program. The computer has eight opcodes; each opcode operates on the following value in memory; some instructions take the operand literally, and some compute a **combo** value from it (equal to register A, B, or C if the value is 4, 5, or 6, respectively; otherwise the value itself). There is a program counter (pc) that increments by 2, unless there is a branch instuction (opcode 3). See the [day's description](https://adventofcode.com/2024/day/17) for details on how the opcodes work. Or look at my `run_program` function, which yields the outputs from running the program:"
+    "Now we have to run the program. The computer has eight opcodes; each opcode operates on the following value in memory; some instructions take the operand literally, and some compute a **combo value** from it.  The combo value is the same as the literal value, except that values 4, 5, and  6 refer to registers A, B, and C, respectively. Opcode 5 outputs (yields) the last octal digit of the combo value. There is a program counter (pc) that increments by 2 on each instruction (to skip over the operand) unless there is a branch instuction (opcode 3). See the [day's description](https://adventofcode.com/2024/day/17) for details on how the opcodes work."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 847,
+   "execution_count": 188,
    "id": "d98f88cc-c435-43fc-bcb5-52e6dd70fdb1",
    "metadata": {},
    "outputs": [],
@@ -7430,12 +6091,12 @@
    "id": "6348d561-9ac9-437c-8bcd-6fbd91d1ebf5",
    "metadata": {},
    "source": [
-    "The answer for Part 1 is easy:"
+    "With my `run_program` function, the answer for Part 1 is easy:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 849,
+   "execution_count": 190,
    "id": "860f24e5-92ad-4361-8920-102ebc573598",
    "metadata": {},
    "outputs": [
@@ -7445,7 +6106,7 @@
        "Puzzle 17.1:   .000 seconds, answer 2,1,0,1,7,2,5,0,3 ok"
       ]
      },
-     "execution_count": 849,
+     "execution_count": 190,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7462,7 +6123,7 @@
    "source": [
     "### Part 2: What is the lowest positive initial value for register A that causes the program to output a copy of itself?\n",
     "\n",
-    "In Part 2, we find that register A has been corrupted, and we need to restore it to the value that will make the program output a copy of itself (a [Quine](https://en.wikipedia.org/wiki/Quine_%28computing%29)). I was afraid of this! AoC always has a puzzle where you have to write an interpreter for a program in some obscure language, but then in Part 2 you have to actually understand what the program is doing; you can't use brute force. (I tried brute force up to A=10,000,000 with no luck.)\n",
+    "In Part 2, we find that register A has been corrupted, and we need to restore it to the value that will make the program output a copy of itself (a [Quine](https://en.wikipedia.org/wiki/Quine_%28computing%29)). I was afraid of this! AoC always has a puzzle where you have to write an interpreter for a program in some obscure language, but then in Part 2 you have to actually *understand* what the program is doing; you can't use brute force. (I tried brute force up to A=10,000,000 with no luck.)\n",
     "\n",
     "To try to understand my program, here it is in pseudocode:\n",
     "\n",
@@ -7484,26 +6145,24 @@
     "\n",
     "So I realized that one octal digit of `A` is eliminated on each pass through the loop, and when `A` hits zero, we exit. Each pass outputs one octal digit, so `A` in octal has to be the same number of digits as my program; 16 octal digits is somewhere in the hundred trillion range. Good thing I gave up on brute force. \n",
     "\n",
-    "I realized that I should go right-to-left, outputing one octal digit at a time, and appending one octal digit at a time to `A`. \n",
-    "\n",
-    "I started playing around like this and found a pattern:"
+    "I started playing around and came up with this:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 851,
+   "execution_count": 192,
    "id": "bb745303-dd20-486f-bbdd-7ae77f995c2c",
    "metadata": {},
    "outputs": [],
    "source": [
-    "def run_with(computer=computer, **kwds) -> Ints: \n",
-    "    \"\"\"Run the program with registers set to the given values.\"\"\"\n",
-    "    return list(run_program(computer._replace(**kwds)))"
+    "def run(computer=computer, **registers) -> List[int]: \n",
+    "    \"\"\"Run the program with registers set as keywords.\"\"\"\n",
+    "    return list(run_program(computer._replace(**registers)))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 852,
+   "execution_count": 193,
    "id": "54ac9b9c-70d9-4356-91c5-40fb285634b4",
    "metadata": {},
    "outputs": [
@@ -7513,7 +6172,7 @@
        "[2, 4, 1, 7, 7, 5, 0, 3, 4, 4, 1, 7, 5, 5, 3, 0]"
       ]
      },
-     "execution_count": 852,
+     "execution_count": 193,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7524,7 +6183,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 853,
+   "execution_count": 194,
    "id": "36d89d9a-c8fc-41be-820b-cb13e40793c0",
    "metadata": {},
    "outputs": [
@@ -7534,18 +6193,18 @@
        "[0]"
       ]
      },
-     "execution_count": 853,
+     "execution_count": 194,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "run_with(A=0o7)   # match the last digit of program"
+    "run(A=0o7)   # match the last digit of program"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 854,
+   "execution_count": 195,
    "id": "892fef38-5f9b-4370-a242-f7a10df5487b",
    "metadata": {},
    "outputs": [
@@ -7555,18 +6214,18 @@
        "[3, 0]"
       ]
      },
-     "execution_count": 854,
+     "execution_count": 195,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "run_with(A=0o72)   # match the last two digits of program"
+    "run(A=0o72)   # match the last two digits of program"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 855,
+   "execution_count": 196,
    "id": "b3d11d5e-30c2-419f-bc11-3f26fbdddfbb",
    "metadata": {},
    "outputs": [
@@ -7576,13 +6235,34 @@
        "[5, 3, 0]"
       ]
      },
-     "execution_count": 855,
+     "execution_count": 196,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "run_with(A=0o726)   # match the last three digits of program"
+    "run(A=0o726)   # match the last three digits of program"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 197,
+   "id": "9ffcefa7-714f-416f-b6c7-8a9ad6d65380",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[5, 5, 3, 0]"
+      ]
+     },
+     "execution_count": 197,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "run(A=0o7266)   # match the last four digits of program"
    ]
   },
   {
@@ -7590,18 +6270,21 @@
    "id": "f40f775f-bb9d-459c-80c3-ac09b6b42904",
    "metadata": {},
    "source": [
-    "That is, if I can pick the right octal digits, then each time I append a digit to the right of `A`, the run of the program outputs one more correct digit of the tail of my program. But there might be several digit values that work for the current digit, but might screw up later. So here's my approach for finding the Quine program:\n",
-    "- I'm going to keep a **set** of candidate values for `A` as the set `As` (because there may be several good digits at each step).\n",
+    "That is, I can build up the right value for `A` to generate a Quine program as follows:\n",
+    "\n",
+    "- I'm going to keep a **set** of candidate partial values for `A` as the set `As`.\n",
     "- The set starts with no digits, so just `{0}`.\n",
-    "- On each iteration I try appending each octal digit to each element of the set `As`.\n",
-    "- I keep the candidate `A` values whose output matches the tail of the program's output.\n",
-    "- Iterate this for each digit and return the set of `A` values that produce the whole program.\n",
-    "- Take the minimum of the set."
+    "- On each iteration I try appending each octal digit to each element of the set `As` (by multplying by 8 and adding the digit).\n",
+    "- I keep the candidate `A` values whose output from the run matches the tail of the program's output.\n",
+    "    - On each iteration we insist on matching one more octal digit of the tail of the program \n",
+    "- Iterate this for each digit in the program and return the set of `A` values that reproduce the whole program.\n",
+    "\n",
+    "All of the resulting `A` values will be Quines, but the puzzle asks us to find just the minimum of the set."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 857,
+   "execution_count": 199,
    "id": "a49c6de9-4e6b-47e5-bcf0-2972a95c1af3",
    "metadata": {},
    "outputs": [
@@ -7611,19 +6294,19 @@
        "Puzzle 17.2:   .004 seconds, answer 267265166222235   ok"
       ]
      },
-     "execution_count": 857,
+     "execution_count": 199,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "def quine(computer) -> Set[int]:\n",
-    "    \"\"\"Find the values of `A` that cause the output to match the program.\"\"\"\n",
+    "    \"\"\"Find the values of register `A` that cause the output of the run to match the program.\"\"\"\n",
     "    As = {0}\n",
     "    for place in reversed(range(len(computer.prog))):\n",
     "        tail = computer.prog[place:]\n",
     "        candidates = {(A * 8) + d for A in As for d in range(8)}\n",
-    "        As = {A for A in candidates if run_with(A=A) == tail}\n",
+    "        As = {A for A in candidates if run(A=A) == tail}\n",
     "    return As\n",
     "\n",
     "answer(17.2, 267265166222235, \n",
@@ -7642,7 +6325,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 859,
+   "execution_count": 201,
    "id": "d14e1966-2feb-4553-9a0a-12595ef4f7d7",
    "metadata": {},
    "outputs": [
@@ -7692,18 +6375,18 @@
     "\n",
     "When a byte falls it creates a barrier. Our task is to find a path that avoids the barriers, from the start in the upper left to the exit in the lower right of a 71 x 71 grid that is the memory board. \n",
     "\n",
-    "This is another search puzzle, like the maze in Day 16, but without the complications (e.g. costs for turning right or left). The puzzle description for today says that we should first consider just the first kilobyte (1024 falling bytes), and I was worried that if I just hand those points to my `Grid` class, it wouldn't cover the whole 71 x 71 grid. Therefore, I created a grid with empty spaces, and then updated with the falling bytes. The function `memory_path` returns a path, and we can then ask for its length to get the answer."
+    "This is another search puzzle, like the maze in Day 16, but without the complications (e.g. costs for turning right or left), so I can use my `GridProblem` class from [AdventUtils](AdventUtils.ipynb) without alteration. The puzzle description for today says that we should first consider just the first kilobyte (1024 falling bytes), and I was worried that if I just hand those points to my `Grid` class, it wouldn't cover the whole 71 x 71 grid. Therefore, I created a grid with empty spaces, and then updated with the falling bytes. The function `memory_path` returns a path, and we can then ask for its length to get the answer."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 861,
+   "execution_count": 203,
    "id": "83af4751-38c9-4830-a2fa-78515b59bc97",
    "metadata": {},
    "outputs": [],
    "source": [
     "def memory_path(falling_bytes: Tuple[Point], width=71, height=71) -> Grid:\n",
-    "    \"\"\"Make a Grid of the given size with the points as obstacles.\"\"\"\n",
+    "    \"\"\"Make a Grid of the given size with the points as obstacles, and find a path.\"\"\"\n",
     "    grid = Grid(['.' * width] * height)\n",
     "    grid.update({p: '#' for p in falling_bytes})\n",
     "    problem = GridProblem(grid=grid, initial=(0, 0), goal=(width - 1, height - 1))\n",
@@ -7712,7 +6395,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 862,
+   "execution_count": 204,
    "id": "29da25e2-f3c2-43e3-8769-1d4fcecb807b",
    "metadata": {},
    "outputs": [
@@ -7722,7 +6405,7 @@
        "Puzzle 18.1:   .014 seconds, answer 344               ok"
       ]
      },
-     "execution_count": 862,
+     "execution_count": 204,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7739,22 +6422,24 @@
    "source": [
     "### Part 2: What are the coordinates of the first byte that will prevent the exit from being reachable from your starting position?\n",
     "\n",
-    "After 1024 bytes fall there is a path from start to exit, but as more bytes fall we might have to switch to a different path, and eventually there will be no path. We're asked for the `x,y` position of the first falling byte that blocks off all paths. I can think of two ways to handle this:\n",
+    "After 1024 bytes fall there is a path from start to exit, but as more bytes fall we might have to switch to a different path, and eventually there will be no path. We're asked for the `(x,y)` position of the first falling byte that blocks off all paths. I can think of two ways to handle this:\n",
     "1) Add falling bytes one at a time and repeat the A-star search each time. **Slow!**\n",
-    "2) Add falling bytes in **binary search** fashion: We know adding no bytes is **good** for getting a path and adding all of them is **bad**; try half way and then update **good** or **bad** depending on whether we found a path. **Fast!**"
+    "2) Add falling bytes in **binary search** fashion: We know adding no bytes is **good** for getting a path and adding all of them is **bad**; try half way and then update **good** or **bad** depending on whether we found a path. Repeat until **good** is one more than **bad**; that's the answer.  **Fast!**"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 864,
+   "execution_count": 206,
    "id": "4c0a8dcb-c3af-45e7-9273-8776e8c3ea1d",
    "metadata": {},
    "outputs": [],
    "source": [
     "def memory_blocker(falling_bytes, good=1024) -> Point:\n",
     "    \"\"\"Which falling byte is the first to block a path to the exit? Do binary search.\"\"\"\n",
-    "    bad  = len(falling_bytes)\n",
-    "    while bad - good > 1:\n",
+    "    # Here `good` and `bad` are the stop values of a slice, not an index,\n",
+    "    # so the final answer is falling_bytes[bad - 1], not falling_bytes[bad]\n",
+    "    bad  = len(falling_bytes) \n",
+    "    while bad != good + 1:\n",
     "        mid = (good + bad) // 2\n",
     "        if memory_path(falling_bytes[:mid]) == search_failure:\n",
     "            bad = mid\n",
@@ -7765,17 +6450,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 865,
+   "execution_count": 207,
    "id": "22371144-5d51-440a-918f-a63de73b13ad",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle 18.2:   .032 seconds, answer 46,18             ok"
+       "Puzzle 18.2:   .033 seconds, answer 46,18             ok"
       ]
      },
-     "execution_count": 865,
+     "execution_count": 207,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7802,12 +6487,22 @@
    "source": [
     "# [Day 19](https://adventofcode.com/2024/day/19): Linen Layout\n",
     "\n",
-    "Today's input is in two sections, the first a list of towel designs (with each letter of a word specifying a color), and the second section a list of desired patterns to be made by adjoining towels."
+    "Today's input is in two sections, the first a list of towel patterns (with each letter of a word specifying a color), and the second a list of desired designs to be made by adjoining towel patterns.  For example, if the patterns include\n",
+    "\n",
+    "     a, dub, rub, ...\n",
+    "\n",
+    "and the desired design is\n",
+    "\n",
+    "     rubadubdub\n",
+    "\n",
+    "then it can be made from the patterns with\n",
+    "\n",
+    "     rub + a + dub + dub"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 868,
+   "execution_count": 210,
    "id": "689df92b-92d7-44e6-8b4e-d67bf3f153df",
    "metadata": {},
    "outputs": [
@@ -7844,14 +6539,14 @@
    "id": "581ff31b-ec09-4ae5-84c7-3b3ffbbd9362",
    "metadata": {},
    "source": [
-    "### Part 1: How many designs are possible?\n",
+    "### Part 1: How many of the desired designs are possible?\n",
     "\n",
-    "The task is to see how many of the designs can posibly be made by concatenating one or more of the patterns (with repetitions allowed). I can do this by checking if some pattern starts the design and recursively checking if the rest of the design is possible:"
+    "The task is to see how many of the desired designs can posibly be made by concatenating one or more of the patterns (with repetitions allowed). I can do this by checking if some pattern starts the design and recursively checking if the rest of the design is possible."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 870,
+   "execution_count": 212,
    "id": "e0b96545-5f60-4c8e-9a0f-c77608c19128",
    "metadata": {},
    "outputs": [],
@@ -7865,7 +6560,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 871,
+   "execution_count": 213,
    "id": "3c3fba1b-d3e5-494e-aad0-42ca0566ae1f",
    "metadata": {},
    "outputs": [
@@ -7875,7 +6570,7 @@
        "Puzzle 19.1:   .040 seconds, answer 242               ok"
       ]
      },
-     "execution_count": 871,
+     "execution_count": 213,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7892,12 +6587,12 @@
    "source": [
     "### Part 2: What do you get if you add up the number of different ways you could make each design?\n",
     "\n",
-    "For Part 2 we need to count all the ways that each design can be made. Since there can be an exponential number of ways for each design, I'm going to `cache` intermediate results. The number of ways is computed by consiering each pattern that starts the design and recursively summing up the count of the number of ways for the rest of the design."
+    "For Part 2 we need to count all the ways that each design can be made. Since there can be an exponential number of ways for each design, I'm going to `cache` intermediate results. The number of ways is computed by considering each pattern that starts the design and recursively summing up the count of the number of ways for the rest of the design."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 873,
+   "execution_count": 215,
    "id": "77d4fae1-d506-4733-9bb2-467619012f97",
    "metadata": {},
    "outputs": [],
@@ -7912,17 +6607,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 874,
+   "execution_count": 216,
    "id": "14116eca-0b0f-484a-a169-9726e4ac7fbf",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle 19.2:   .185 seconds, answer 595975512785325   ok"
+       "Puzzle 19.2:   .189 seconds, answer 595975512785325   ok"
       ]
      },
-     "execution_count": 874,
+     "execution_count": 216,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7937,12 +6632,12 @@
    "id": "b1199e79-bb09-4d68-89e6-b235c5f987c5",
    "metadata": {},
    "source": [
-    "That was so easy that I'm willing to explore a bit more. First, here's a check that says a design is possible if and only if there is at least one way to make it: "
+    "That was so easy that there is time to explore a bit more. First, here's a check that says a design is possible if and only if there is at least one way to make it: "
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 876,
+   "execution_count": 218,
    "id": "f992b197-be14-47dc-8678-10cc63a1afd7",
    "metadata": {},
    "outputs": [],
@@ -7956,34 +6651,42 @@
    "id": "a003849a-ae35-4c86-8d48-b954908d636b",
    "metadata": {},
    "source": [
-    "Here is an alternative approach to Part 1 that turns out to be faster. It uses one big regular expression to match against all the designs. The regular expression matches one or more repetitions of one of the patterns, as a whole-line match. This is matched against all the designs, concatened together with newlines. We do this all in one call to `re.compile` and one call to `findall`, to keep as much as possible running in the C library rather than in user-written Python code. (Unfortunately, this approach cannot be applied directly to Part 2.)"
+    "Here is an alternative approach to Part 1 that turns out to be faster. It uses one big regular expression to match repetitions of the designs. We then check for a full-line match against each of the desired designs. (Unfortunately, this approach cannot be applied directly to Part 2.)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 878,
-   "id": "57296f79-d0a0-4de3-bb1c-b3ed84ba1a59",
+   "execution_count": 220,
+   "id": "2437ae06-27e4-4840-ad51-65454ef0bf60",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def count_possible_designs(designs, patterns) -> int:\n",
+    "    \"\"\"A count of all the `designs` that can be made by concatenating `patterns`.\"\"\"\n",
+    "    fullmatch = re.compile(\"(\" + \"|\".join(patterns) + \")+\").fullmatch\n",
+    "    return quantify(designs, fullmatch)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 221,
+   "id": "88e45604-ce45-478e-a1b8-66ead1d0e72e",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle 19.1:   .002 seconds, answer 242               ok"
+       "Puzzle 19.1:   .004 seconds, answer 242               ok"
       ]
      },
-     "execution_count": 878,
+     "execution_count": 221,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "def possible_designs(designs, patterns) -> List[str]:\n",
-    "    \"\"\"All the `designs` that can be made by concatenating `patterns`.\"\"\"\n",
-    "    regex = re.compile(r\"^(\" + \"|\".join(patterns) + r\")+$\", re.MULTILINE)\n",
-    "    return regex.findall('\\n'.join(designs))\n",
-    "\n",
-    "answer(19.1, 242, lambda:\n",
-    "       len(possible_designs(designs, patterns)))"
+    "answer(19.1, 242, lambda: \n",
+    "       count_possible_designs(designs, patterns))"
    ]
   },
   {
@@ -7998,7 +6701,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 880,
+   "execution_count": 223,
    "id": "156dcbf7-79ec-41a7-a9f2-397a827b9856",
    "metadata": {},
    "outputs": [
@@ -8032,16 +6735,16 @@
    "source": [
     "### Part 1: How many cheats would save you at least 100 picoseconds?\n",
     "\n",
-    "We are told that the grid depicts a single path from start (`S`) to end (`E`). Each step (in one of the four cardinal directions) takes one picosecond. But you are allowed to cheat once during the race by going through a wall: you can take two steps where the first step is into a wall and the second is back on the track. We are asked how many such cheats would save 100 picoseconds or more.\n",
+    "We are told that the grid depicts a single path from start (`S`) to end (`E`). Each step (in one of the four cardinal directions) takes one picosecond. But you are allowed to **cheat** once during the race by going through a wall: you can take two steps where the first step is into a wall and the second is back on the track. We are asked how many such cheats would save 100 picoseconds or more.\n",
     "\n",
-    "This is an all-paths-to-the-goal puzzle, which should make you think [Dijkstra's algorithm](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm). My function `dijkstra` will return a dict of `{(x, y): distance_to_end}`. It works by maintaining a queue, `Q` of points to be considered, and one at a time popping a point off the queue, and for each neighbor that is not a wall, add the neighbor to the queue and record the distance to the neighbor as being one more than the distance to the point in the dict `D`. Since we are told the grid is single-path, we don't have to worry about updating entries in `D` for a second path to a point.\n",
+    "This is an all-paths-to-the-goal puzzle, which should make you think [**Dijkstra's algorithm**](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm). My function `dijkstra` will return a dict of `{(x, y): distance_to_end}`. It works by maintaining a queue, `Q` of points to be considered, and one at a time popping a point off the queue, and for each neighbor that is not a wall, add the neighbor to the queue and record the distance to the neighbor as being one more than the distance to the point in the dict `D`. Since we are told the grid is single-path, we don't have to worry about updating entries in `D` for a second path to a point.\n",
     "\n",
     "Then my function `cheats` yields all `(start_position, end_position, time_saved)` tuples where the time saved is at least the given lower bound."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 882,
+   "execution_count": 225,
    "id": "4c4ef05c-b548-49f9-b092-847e9752e745",
    "metadata": {},
    "outputs": [],
@@ -8059,29 +6762,30 @@
     "                D[p2] = D[p] + 1\n",
     "    return D\n",
     "\n",
-    "def cheats(racetrack, lower_bound=1) -> Iterable[Tuple[Point, Point, int]]:\n",
-    "    \"\"\"All ways of cheating by taking one step onto a wall (at p2) and a second step back on track (at p3).\"\"\"\n",
-    "    D = dijkstra(racetrack, 'E')\n",
+    "def cheats(racetrack, minimum_savings=1) -> Iterable[Tuple[Point, Point, int]]:\n",
+    "    \"\"\"All ways of cheating by taking one step onto a wall (at p2) and a second step back on track (at p3),\n",
+    "    as long as they save at lease `minimum_savings` picoseconds\"\"\"\n",
+    "    D = dijkstra(racetrack, 'E') # A dict of {start_position: distance_to_E}\n",
     "    return ((p1, p3, t)\n",
     "            for p1 in D\n",
     "            for p2 in racetrack.neighbors(p1) if racetrack[p2] == '#'\n",
     "            for p3 in racetrack.neighbors(p2)\n",
-    "            if  p3 in D and (t := D[p1] - D[p3] - 2) >= lower_bound)"
+    "            if  p3 in D and (t := D[p1] - D[p3] - 2) >= minimum_savings)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 883,
+   "execution_count": 226,
    "id": "1bbd8b72-c503-4384-aaea-a5bed45a4491",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle 20.1:   .029 seconds, answer 1343              ok"
+       "Puzzle 20.1:   .028 seconds, answer 1343              ok"
       ]
      },
-     "execution_count": 883,
+     "execution_count": 226,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -8096,41 +6800,42 @@
    "id": "0f86c3a4-47e7-4731-8acf-9133b3e41838",
    "metadata": {},
    "source": [
-    "At first I had a puzzling **bug**. I had a lot of confidence in my code, so I addressed it by carefully re-reading the puzzle description. Then I realized my mistake: I didn't count the 2 picoseconds of cheating as part of the total time. I fixed that by inserting the \"`-2`\" in the last line of `cheats`. In the process of carefully re-reading, I realized that the path through the grid is a single path; I didn't need a queue of points in `dijkstra`; the queue will always be just one point. But changing it wouldn't have a big effect on efficiency, so I'll keep it as is.\n",
+    "At first I had a puzzling **bug**. I had a lot of confidence in my code, but AoC said I had the wrong answer. I addressed it by carefully re-reading the puzzle description. Then I realized my mistake: I didn't count the 2 picoseconds of cheating as part of the total time. I fixed that by inserting the \"`-2`\" in the last line of `cheats`. In the process of carefully re-reading, I realized that the path through the grid is a single path; I didn't need a queue of points in `dijkstra`; the queue will always be just one point. But changing it wouldn't have a big effect on efficiency, so I'll keep it as is.\n",
     "\n",
     "<img src=\"https://files.mastodon.social/media_attachments/files/113/686/544/560/665/267/small/41dc36dd2b873d41.jpg\" width=400>\n",
     "\n",
     "\n",
     "### Part 2: How many big cheats would save you at least 100 picoseconds?\n",
     "\n",
-    "In Part 2 you can use a much bigger cheat, of up to 20 steps (and thus 20 picoseconds). But you can still only use one cheat. I'll tackle this by looking at all points in a neighborhood of radius 20 from each starting point on the path."
+    "In Part 2 you can use a much **bigger cheat**, of up to 20 steps (and thus 20 picoseconds). But you can still only use one cheat. I'll tackle this by looking at all points in a neighborhood of radius 20 from each starting point on the path."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 885,
+   "execution_count": 228,
    "id": "d370e24c-9b82-4415-82a5-7afe2be17654",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle 20.2:   .757 seconds, answer 982891            ok"
+       "Puzzle 20.2:   .773 seconds, answer 982891            ok"
       ]
      },
-     "execution_count": 885,
+     "execution_count": 228,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "def big_cheats(racetrack, lower_bound=1, radius=20) -> Iterable[Tuple[Point, Point, int]]:\n",
-    "    \"\"\"All ways of cheating by taking up to `radius` steps through walls and back to the track.\"\"\"\n",
-    "    D = dijkstra(racetrack, 'E')\n",
+    "def big_cheats(racetrack, minimum_savings=1, radius=20) -> Iterable[Tuple[Point, Point, int]]:\n",
+    "    \"\"\"All ways of cheating by taking up to `radius` steps through walls and back to the track,\n",
+    "    as long as they save at lease `minimum_savings` picoseconds\"\"\"\n",
+    "    D = dijkstra(racetrack, 'E') # A dict of {start_position: distance_to_E}\n",
     "    return ((p1, p2, t)\n",
     "            for p1 in D\n",
     "            for p2 in neighborhood(p1, radius)\n",
-    "            if  p2 in D and (t := D[p1] - D[p2] - taxi_distance(p1, p2)) >= lower_bound)\n",
+    "            if  p2 in D and (t := D[p1] - D[p2] - taxi_distance(p1, p2)) >= minimum_savings)\n",
     "\n",
     "def neighborhood(point, radius) -> List[Point]:\n",
     "    \"\"\"All points within `radius` of `point` (using taxi distance).\"\"\"\n",
@@ -8153,7 +6858,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 887,
+   "execution_count": 230,
    "id": "332e9c72-db9a-4b90-a649-45f7bf955e84",
    "metadata": {},
    "outputs": [
@@ -8163,7 +6868,7 @@
        "Puzzle 20.1:   .023 seconds, answer 1343              ok"
       ]
      },
-     "execution_count": 887,
+     "execution_count": 230,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -8185,7 +6890,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 889,
+   "execution_count": 232,
    "id": "9d0eea9f-9d8f-4410-97ec-13d8b136925b",
    "metadata": {},
    "outputs": [
@@ -8215,7 +6920,7 @@
    "source": [
     "### Part 1: What is the sum of the complexities of the five codes on your list?\n",
     "\n",
-    "We know the codes, so what is the difficulty? Unfortunately, the numeric keypad is inaccessible, so we have to get a **robot** to press the buttons, and we have to command the robot's arm by pressing some buttons on a **remote control directional keypad**: arrow keys to move the arm, and the \"`A`\" (activate) button to make the arm press the button it is currently pointing at. Here are the two keypads:\n",
+    "We know the codes, so what is the difficulty? It turns out the numeric keypad is inaccessible, so we have to get a **robot** to press the buttons, and we have to command the robot's arm by pressing some buttons on a **remote control directional keypad**: arrow keys to move the arm, and the \"`A`\" (activate) button to make the arm press the button it is currently pointing at. Here are the two keypads:\n",
     "\n",
     "        +---+---+---+            +---+---+\n",
     "        | 7 | 8 | 9 |            | ^ | A |\n",
@@ -8234,28 +6939,32 @@
     "- Robot 2 presses some buttons on Robot 1's remote keypad (e.g. \"<A^A^^AvvvA\")\n",
     "- Robot 1 presses some buttons on the door's numeric keypad (e.g. \"029A\").\n",
     "\n",
-    "The robots all initially have their arm pointing at the `'A'` key of their respective target keypads. You command them to move the arm by pressing an arrow key on their remote, and command them to press the current button by pressing the `'A'` key.\n",
+    "The robots all initially have their arm pointing at the `'A'` key of their respective target keypads. It is forbidden to command the arm to go off the keypad or to go to the empty position.\n",
     "\n",
     "We'd like to find the shortest possible sequence of button presses at the top level. Once we've figured out the shortest button sequence to enter each of the codes, we have to compute the **complexity** of each code, which is defined as the integer part of the code times the length of the shortest possible sequence.\n",
     "\n",
     "Here are some considerations:\n",
     "- To get from one button to the next there can be several paths.\n",
-    "- For example, to get from \"A\" to \"7\" the shortest paths include \"^^^<<\" and \"^<^<^\" and \"<^<^^\" (but not \"<<^^^\", because that would hit the empty position, which is forbidden.\n",
+    "- For example, to get from \"A\" to \"7\" on the numeric keypad the shortest paths include \"^^^<<\" and \"^<^<^\" and \"<^<^^\".\n",
+    "    - (But not \"<<^^^\", because that would hit the empty position, which is forbidden.)\n",
+    "    - (Also not any sequences with a \">\" or \"v\" button, because that's just wasteful.)\n",
     "- Each of these paths have the same length, so if we were directly pressing Robot 1's remote control, any path would do.\n",
     "- However, it might take the robot at the next level a different number of presses to command each of these paths.\n",
     "- To command \"^^^\" the next robot has to command this robot to the \"^\" key and then press \"AAA\". If the \"^\" and \"<\" keys are interspersed, the commands will take more buttons, because there will be navigation between each \"A\". Therefore, I will consider at most two paths: all the horizontal arrows first, then all the veertical, or vice versa.\n",
-    "- Fortunately, whenever there is a button press on the numeric keypad, we know that the robots on all the higher-level remote keypads are at \"A\", because each one must have activated a button press to make it all happen.\n",
-    "- Therefore, the parts of the problem are *decomposible*: we can optimize \"get the robot arm from the current position to the desired position\" and that will not depend on the solutions to other subparts of the problem.\n",
-    "- I'm guessing that in Part 2 the button sequences will be ridiculously long, so I'll look for an efficient representations.\n",
-    "    - If Part 2 needs to know something about the actual presses, we could represent it as a `Counter` of start+destination subtasks. For example, if the task is to press \"0909A\", and we always start at \"A\", then we can represent this as `{'A0': 1, '09: 2, '90': 2, '9A': 1}`.\n",
-    "    - If Part 2 only needs to know the total number of button presses, then we don't need to explicitly represent the button presses, we just need to count them. I'm going to guess that that will be the case; we're likely to get many more robots and/or keyboards.\n",
+    "- Fortunately, whenever there is a button press on the numeric keypad, we know that *all* the robots are on \"A\", because each one must have activated a button press to make the chain of presses happen.\n",
+    "- Therefore, the parts of the problem are *decomposible*: we can optimize the command [get the robot arm from the \"^\" to the \"A\"] and that will not depend on the solutions to other subparts of the problem.\n",
     "\n",
-    "I could represent a keypad with my `Grid` class, but I don't need what the Grid provides, all I need is a way to look up the (x, y) location of each key. I'll also explicitly save the (x, y) position of the forbidden empty spot as `keypad.avoid`."
+    "\n",
+    "I'm guessing that in Part 2 the button sequences will be ridiculously long, so I'll look for an efficient representations.\n",
+    "- If Part 2 needs to know something about the actual presses, we could represent it as a `Counter` of start+destination subtasks. For example, if the task is to press \"0909A\", and we always start at \"A\", then we can decompose that into \"A-to-0, 0-to-9, 9-to-0, 0-to-9, 9-to-A\" and represent this as `{'A0': 1, '09: 2, '90': 2, '9A': 1}`. There are only 5 keys on the numeric keypad, so only 20 different movements, so even if a button sequence has trillions of presses, we can represent it as a Counter with no more than 20 items.\n",
+    "- If Part 2 only needs to know the total number of button presses, then we don't need to explicitly represent the button presses, we just need to count them. I'm going to guess that that will be the case; we're likely to get many more robots and/or keyboards.\n",
+    "\n",
+    "I could represent a keypad with my `Grid` class, but I don't need what the Grid provides, all I need is a way to look up the (x, y) location of each key. I'll also explicitly save the (x, y) position of the forbidden empty position as `keypad.avoid`."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 891,
+   "execution_count": 234,
    "id": "779c6b4c-ceb0-49ac-96f2-4700835c70ea",
    "metadata": {},
    "outputs": [],
@@ -8276,18 +6985,18 @@
    "id": "486ae303-36cf-4750-965b-3402eec2b625",
    "metadata": {},
    "source": [
-    "Now I can compute the possible paths from any starting key to any destination key on a keypad, and press the destination key. There will be either one or two paths, depending on whether one of them hits the `avoid` spot."
+    "Now I can compute the remote keypad presses that are required to command a robot to move from `key1` to `key2` and press `key2`.  There will be either one or two possible paths, depending on whether one of them hits the `avoid` spot."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 893,
+   "execution_count": 236,
    "id": "c915ada2-9dfe-42fe-bd08-855ff5d0e837",
    "metadata": {},
    "outputs": [],
    "source": [
     "def possible_paths(key1, key2, keypad) -> Iterable[str]:\n",
-    "    \"\"\"Should we try, e.g. \">>^\" or \"^>>\", or both, to get from key1 to key2 on keypad?\"\"\"\n",
+    "    \"\"\"Should we try, e.g. \">>^^A\" or \"^^>>A\", or both, to start at key1 and press key2 on keypad?\"\"\"\n",
     "    pos1, pos2 = keypad[key1], keypad[key2]\n",
     "    (dx, dy) = sub(pos2, pos1)\n",
     "    horizontal = abs(dx) * ('>' if dx > 0 else '<')\n",
@@ -8298,9 +7007,19 @@
     "        yield vertical + horizontal + 'A'"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "e9243a77-8466-4aea-bbc9-b10af141e2fb",
+   "metadata": {},
+   "source": [
+    "My first **bug** on today's puzzle was multiplying the arrow character by `dx` instead of `abs(dx)`. Did you know that `-2 * '>'` is the empty string, and not an error? \n",
+    "\n",
+    "Here are some examples of usage:"
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 894,
+   "execution_count": 238,
    "id": "391f6120-6373-43f2-b697-585c90e45e54",
    "metadata": {},
    "outputs": [],
@@ -8315,19 +7034,19 @@
    "id": "74f1f872-5c0c-4baa-a941-d910dc9c1048",
    "metadata": {},
    "source": [
-    "We need to compute the **complexity** of a code for our final answer:"
+    "We will need to compute the **complexity** of a code for our final answer:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 896,
+   "execution_count": 240,
    "id": "1e2e8c59-744f-4f36-9251-c8ea5fd60aed",
    "metadata": {},
    "outputs": [],
    "source": [
-    "def complexity(code, num_presses: int): \n",
-    "    \"\"\"The integer part of the code times the (niminimum) number of key presses.\"\"\"\n",
-    "    return int(cat(digits(code))) * num_presses"
+    "def complexity(code, levels=4): \n",
+    "    \"\"\"The integer part of the code times the niminimum number of key presses.\"\"\"\n",
+    "    return int(cat(digits(code))) * min_keypresses(code, levels)"
    ]
   },
   {
@@ -8335,42 +7054,36 @@
    "id": "975b5719-9afc-4b0a-9e07-c1c2b38059f7",
    "metadata": {},
    "source": [
-    "And here's how we compute the minimum number of keypresses. Normally I would do this with a `@cache` decorator, but I was encountering **bugs** doing it that way and got confused (off-by-one errors, maybe?), so I refactored to explicitly create a cache of path lengths. The cache says  how many button presses it takes at each level to command a single button press, getting you from the start button to the destination button and pressing the destination button. This approach made debugging  easier for me, or maybe it was just starting over fresh that made it easier."
+    "And here's how we compute the minimum number of keypresses. "
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 898,
-   "id": "704ade67-31e6-4f39-b48c-0a7185c42c48",
+   "execution_count": 242,
+   "id": "980572de-2589-4ada-a2a1-6c17cc627353",
    "metadata": {},
    "outputs": [],
    "source": [
-    "def min_keypresses(code: str, levels: int, numeric_keypad=numeric_keypad, remote_keypad=remote_keypad) -> int:\n",
-    "    \"\"\"The number of keypresses to type `code`, going through `levels`.\"\"\"\n",
-    "    def total_presses(keys: str, level: int) -> int:\n",
-    "        return sum(one_button_path_lengths[level, key1, key2] \n",
-    "                   for key1, key2 in sliding_window('A' + keys, 2))\n",
-    "    ## Initializing the one_button_path_lengths[level, key1, key2] dict\n",
-    "    one_button_path_lengths = {(0, key1, key2): 1\n",
-    "                               for key1 in remote_keypad for key2 in remote_keypad}\n",
-    "    for level in range(1, levels):\n",
-    "        keypad = numeric_keypad if level == levels - 1 else remote_keypad\n",
-    "        for key1 in keypad:\n",
-    "            for key2 in keypad:\n",
-    "                paths = possible_paths(key1, key2, keypad)\n",
-    "                one_button_path_lengths[level, key1, key2] = min(total_presses(path, level - 1) for path in paths)\n",
-    "    ## The cache is built, so just add up the one_button_path_lengths.\n",
-    "    return total_presses(code, levels - 1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 899,
-   "id": "4d8c8659-52d3-4349-8465-7003e880502f",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "assert list(sliding_window('A029A', 2)) == ['A0', '02', '29', '9A'] # All the start+destination pairs from the code."
+    "def min_keypresses(code: str, levels: int) -> int:\n",
+    "    \"\"\"The smallest possible number of keypresses to type `code`, if there are `levels`\n",
+    "    of button-pressers (one of them you, the rest robots).\"\"\"\n",
+    "    \n",
+    "    def total_presses(keysequence: str, level: int) -> int:\n",
+    "        \"\"\"Total presses required to command `keysequence` from this level.\"\"\"\n",
+    "        return sum(one_button_min_keypresses(level, key1, key2)\n",
+    "                   for key1, key2 in sliding_window('A' + keysequence, 2))\n",
+    "        \n",
+    "    @cache\n",
+    "    def one_button_min_keypresses(level, key1, key2) -> int:\n",
+    "        \"\"\"The minimum number of presses to command a press of key2, starting from key1.\"\"\"\n",
+    "        if level == 1: # Just press it!\n",
+    "            return 1 \n",
+    "        else:          # Command it!\n",
+    "            target_keypad = numeric_keypad if level == levels else remote_keypad\n",
+    "            return min(total_presses(path, level - 1) \n",
+    "                       for path in possible_paths(key1, key2, target_keypad))\n",
+    "\n",
+    "    return total_presses(code, levels)"
    ]
   },
   {
@@ -8383,24 +7096,54 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 901,
+   "execution_count": 244,
    "id": "393a8c6b-6a1c-4495-aad5-92f48711fbf1",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle 21.1:   .002 seconds, answer 205160            ok"
+       "Puzzle 21.1:   .000 seconds, answer 205160            ok"
       ]
      },
-     "execution_count": 901,
+     "execution_count": 244,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "answer(21.1, 205160, lambda:\n",
-    "       sum(complexity(code, min_keypresses(code, levels=4)) for code in codes))"
+    "       sum(map(complexity, codes)))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "89a0f647-3c3d-4476-a434-1ab36de65831",
+   "metadata": {},
+   "source": [
+    "This is what `sliding_window` does: gives (start-key + destination-key) pairs. And here are some small examples."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 246,
+   "id": "4d8c8659-52d3-4349-8465-7003e880502f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "assert list(sliding_window('A029A', 2)) == ['A0', '02', '29', '9A']\n",
+    "\n",
+    "assert min_keypresses('029A', 1) ==  4 # \"029A\"\n",
+    "assert min_keypresses('029A', 2) == 12 # \"<A^A>^^AvvvA\"\n",
+    "assert min_keypresses('029A', 3) == 28 # \"v<<A>>^A<A>AvA<^AA>A<vAAA>^A\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "08d46094-0ebf-4c84-8ec4-b563630b2458",
+   "metadata": {},
+   "source": [
+    "I was encountering other **bugs** (off-by-one errors, maybe?), so I wrote some code that explicitly built a cache of path lengths. Once I did that I understood the puzzle better and was able to easily write the code above with the cache handled by the decorator, which is a little cleaner."
    ]
   },
   {
@@ -8408,31 +7151,31 @@
    "id": "2a16c8f8-e1e5-47f8-b6c6-4a7500a457e6",
    "metadata": {},
    "source": [
-    "### Part 2: Now, what is the sum of the complexities of the five codes on your list?\n",
+    "### Part 2: With 27 levels, what is the sum of the complexities of the five codes on your list?\n",
     "\n",
-    "As I suspected, Part 2 gets us into the ridiculous number of button presses. The problem is the same, but now there are **27** levels, not 4. No new code, just sum the complexity of the `min_keypresses` again:"
+    "As I suspected, Part 2 gets us into a [ludicrous](https://www.youtube.com/watch?v=oApAdwuqtn8) number of button presses. The problem is the same, but now there are **27** levels, not **4**. No new code, just sum the complexity  again:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 903,
+   "execution_count": 249,
    "id": "563c5959-692d-4368-8c0b-469fa0142678",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle 21.2:   .008 seconds, answer 252473394928452   ok"
+       "Puzzle 21.2:   .004 seconds, answer 252473394928452   ok"
       ]
      },
-     "execution_count": 903,
+     "execution_count": 249,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "answer(21.2, 252473394928452, lambda:\n",
-    "       sum(complexity(code, min_keypresses(code, levels=27)) for code in codes))"
+    "       sum(complexity(code, levels=27) for code in codes))"
    ]
   },
   {
@@ -8445,7 +7188,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 905,
+   "execution_count": 251,
    "id": "f2d29a66-5420-4fc1-8586-1570ed5ac0a8",
    "metadata": {},
    "outputs": [
@@ -8455,7 +7198,7 @@
        "439646398242"
       ]
      },
-     "execution_count": 905,
+     "execution_count": 251,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -8469,7 +7212,7 @@
    "id": "1cf2d848-2f43-48dc-8862-493cebd94558",
    "metadata": {},
    "source": [
-    "If we could press one button per millisecondsecond, it would only take 14 years to do this number of button presses."
+    "If we could press one button per millisecond, it would take [**14 years**](https://www.google.com/search?q=439646398242+milliseconds+in+years) to do this number of button presses."
    ]
   },
   {
@@ -8484,7 +7227,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 908,
+   "execution_count": 254,
    "id": "2c1e7612-4ec5-4ce1-b591-5c3a14f8ea61",
    "metadata": {},
    "outputs": [
@@ -8535,7 +7278,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 910,
+   "execution_count": 256,
    "id": "3807adbc-261a-4108-88ba-6e2b061526b5",
    "metadata": {},
    "outputs": [],
@@ -8551,17 +7294,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 911,
+   "execution_count": 257,
    "id": "fce754cd-f6da-4e7d-b406-3314c9c28ca8",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle 22.1:   .305 seconds, answer 14273043166       ok"
+       "Puzzle 22.1:   .325 seconds, answer 14273043166       ok"
       ]
      },
-     "execution_count": 911,
+     "execution_count": 257,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -8580,16 +7323,17 @@
     "\n",
     "### Part 2: What is the most bananas you can get?\n",
     "\n",
-    "Knowing the timeline of secret numbers is not the whole story. Each buyer monkey has a **price** in bananas that they are offering at each time step. The price is the ones digit of their secret number (e.g., for secret number 9524047 the price is 7 bananas). Each monkey wants to buy exactly one hiding spot. We would like to wait for the highest price from each monkey, but we don't speak monkeese. We do have a translator who speaks a few words, put unfortunately, the translator doesn't know enough to help us sell as soon as the price hits 9 (or 8, or whatever). The translator has only the ability to help as follows:\n",
+    "Knowing the timeline of secret numbers is not the whole story. Each buyer monkey has a **price** in bananas that they are offering at each time step. The price is the ones digit of their secret number (e.g., for secret number 9524047 the price is 7 bananas). Each monkey wants to buy exactly one hiding spot. We would like to wait for the highest price offering from each monkey, but we don't speak monkeese. We do have a translator who speaks a few words, but unfortunately, the translator doesn't know enough to help us sell as soon as the price hits 9 (or 8, or whatever). The translator has only the ability to help as follows:\n",
     "- We tell the translator to watch for a specific sequence of four deltas in price from one time step to the next for the first monkey.\n",
     "    -  For example, watch for the deltas (**+1, -2, 0, +3**) in the price timeline.\n",
     "- As soon as that sequence of 4 deltas appears in a monkey's price timeline, we sell that monkey  a hiding spot for the current price.\n",
     "    - For example, if the prices are (3, 3, 3, 5, 6, 4, 4, 7, ...) then the deltas are (0, 0, +2, **+1, -2, 0, +3**, ...) and we sell for 7 bananas.\n",
+    "    - That monkey is now done and won't buy again.\n",
     "- The translator simultaneously monitors all the monkeys.\n",
     "\n",
     "Our task is to get the most possible bananas under these constraints. \n",
     "\n",
-    "Can we brute-force it? Each delta is between -9 and +9, so the number of possible 4-tuples of deltas is 19<sup>4</sup> or about 100,000; a small number. However, if for each possible 4-tuple of deltas I looked at all 2000 steps of all 1685 monkeys, then 19<sup>4</sup> * 2000 * 1685 is more than 400 billion, which is a medium-large number. So instead I'll do this:\n",
+    "Can we brute-force it? Each delta is between -9 and +9, so the number of possible 4-tuples of deltas is 19<sup>4</sup> or about 100,000; a small number. However, if for each possible 4-tuple of deltas I looked at all 2000 steps of all 1685 monkeys, then 19<sup>4</sup> ✖️ 2000 ✖️ 1685 is more than 400 billion, which is a medium-large number. So instead I'll do this:\n",
     "\n",
     "    For each monkey:\n",
     "        For each 4-tuple of price deltas in the monkey's price timeline:\n",
@@ -8608,7 +7352,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 913,
+   "execution_count": 259,
    "id": "cbbb4793-b13d-4a95-ba03-673b3ebaa229",
    "metadata": {},
    "outputs": [],
@@ -8641,17 +7385,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 914,
+   "execution_count": 260,
    "id": "34eaf7fe-fe9b-4858-b1e8-e4c3713ea093",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle 22.2:  1.295 seconds, answer 1667              ok"
+       "Puzzle 22.2:  1.285 seconds, answer 1667              ok"
       ]
      },
-     "execution_count": 914,
+     "execution_count": 260,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -8671,7 +7415,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 916,
+   "execution_count": 262,
    "id": "a2da8c78-d240-4c52-a83a-f3599f4f69a4",
    "metadata": {},
    "outputs": [
@@ -8681,7 +7425,7 @@
        "(-3, 2, -1, 2)"
       ]
      },
-     "execution_count": 916,
+     "execution_count": 262,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -8702,7 +7446,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 918,
+   "execution_count": 264,
    "id": "9de3f365-c546-494a-a18c-2ae58d88792b",
    "metadata": {},
    "outputs": [
@@ -8710,13 +7454,13 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "271 monkeys (16%), price 6.2 mean: {1: 0, 2: 0, 3: 43, 4: 34, 5: 33, 6: 32, 7: 37, 8: 42, 9: 50}\n"
+      "271 monkeys (16%), price 6.2 mean: {0: 0, 1: 0, 2: 0, 3: 43, 4: 34, 5: 33, 6: 32, 7: 37, 8: 42, 9: 50}\n"
      ]
     }
    ],
    "source": [
     "prices = [p for secret in secrets for d, p in price_timeline(secret).items() if d == best]\n",
-    "histo  = {p: prices.count(p) for p in range(1, 10)}\n",
+    "histo  = {p: prices.count(p) for p in range(10)}\n",
     "print(f'{len(prices)} monkeys ({len(prices)/len(secrets):.0%}), price {mean(prices):3.1f} mean: {histo}')"
    ]
   },
@@ -8725,14 +7469,14 @@
    "id": "7fac136e-b676-49c9-91f1-a209b9ef53fa",
    "metadata": {},
    "source": [
-    "We do pretty well on prices, getting a lot of 8 and 9 prices, but only 16% of monkeys every get this sequence of price deltas.\n",
+    "We do pretty well on prices, getting a lot of 8 and 9 prices, and nothing less than 3, but only 16% of monkeys every get this sequence of price deltas.\n",
     "\n",
     "Do any 4-tuples show up in more timelines?"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 920,
+   "execution_count": 266,
    "id": "4fc191f9-62d8-47ef-a571-8c0541e25f4d",
    "metadata": {},
    "outputs": [
@@ -8751,14 +7495,13 @@
        " ((1, -1, 0, 0), 292)]"
       ]
      },
-     "execution_count": 920,
+     "execution_count": 266,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "counts = Counter(delta for secret in secrets for delta in price_timeline(secret))\n",
-    "counts.most_common(10)"
+    "Counter(append(map(price_timeline, secrets))).most_common(10)"
    ]
   },
   {
@@ -8766,7 +7509,38 @@
    "id": "1fa741c6-ecf7-4459-a017-ffa574352d7e",
    "metadata": {},
    "source": [
-    "Yes, but not by much, and they are mostly negative-trending 4-tuples. I guess that's why they yielded lower totals."
+    "Yes, but not by that much: 322 monkeys is 19% more than the 271 monkeys for the best 4-tuple, but the total number of bananas is less:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 268,
+   "id": "bbd329a0-309c-4c81-a780-6bd97a95f652",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "1341"
+      ]
+     },
+     "execution_count": 268,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "bananas[(0, -1, 1, -1)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 269,
+   "id": "4a6a5116-2e01-46af-adf2-96ebd0a53e5f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "del bananas # clean up"
    ]
   },
   {
@@ -8781,7 +7555,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 923,
+   "execution_count": 271,
    "id": "85f5b145-8c5e-448c-8b45-ad5750252ff2",
    "metadata": {},
    "outputs": [
@@ -8827,12 +7601,12 @@
    "source": [
     "### Part 1: Find all the sets of three inter-connected computers. How many contain at least one computer with a name that starts with t?\n",
     "\n",
-    "We're asked to find three inter-connected computers, e.g., three computers A, B, C, such that A-B, B-C, and C-A are all in the list of connections (but connections are bidirectional, so either C-A or A-C could be in the input). A set where every node is connected to every other is called a **clique**. I'll represent the network **graph** as a dict of the form `{A: {B, C}}` to denote that node `A` is connected to `B` and `C`. The function `bidrected_graph` forms a graph from an iterable of (A, B) connections. Then `triples_starting_with` finds all cliques of size 3, where at least one of them starts with the given letter. The answer for Part 1 is then the number of triples that start with `t`."
+    "We're asked to find three inter-connected computers, e.g., three computers A, B, C, such that A-B, B-C, and C-A are all in the list of connections (but connections are bidirectional, so either A-B or B-A could be in the input). A set where every node is connected to every other is called a **clique**. I'll represent the network **graph** as a dict of the form `{A: {B, C}}` to denote that node `A` is connected to `B` and `C`. The function `bidrected_graph` forms a graph from an iterable of (A, B) connections. Then `triples_starting_with` finds all cliques of size 3, where at least one of them starts with the given letter. The answer for Part 1 is then the number of triples that start with `t`."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 925,
+   "execution_count": 273,
    "id": "289d2325-1e58-41f5-b4b2-b90ae26e7887",
    "metadata": {},
    "outputs": [],
@@ -8857,7 +7631,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 926,
+   "execution_count": 274,
    "id": "6425577d-4ca9-45de-9698-cd9b026f7ce6",
    "metadata": {},
    "outputs": [
@@ -8867,7 +7641,7 @@
        "Puzzle 23.1:   .001 seconds, answer 1170              ok"
       ]
      },
-     "execution_count": 926,
+     "execution_count": 274,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -8884,12 +7658,12 @@
    "source": [
     "### Part 2: What is the password to get into the LAN party?\n",
     "\n",
-    "In Part 2 we learn two important facts. First, the LAN party is the largest **clique** in the graph. Second, the **password** is formed by listing the names of all the computers in the LAN party in alphabetical order, and separating them by commas. The function `maximum_clique` finds the largest clique; and `password` creates the password. The function `expand_clique` takes a node, a graph, and a partially-formed clique. It adds the node to the clique, and recursively looks for and adds any other nodes that should be added, finally returning the clique."
+    "In Part 2 we are asked to figure out the password for the LAN party. We learn two important facts. First, the LAN party is the largest **clique** in the graph. Second, the **password** is formed by listing the names of all the computers in the LAN party in alphabetical order, separatied by commas. The function `maximum_clique` finds the largest clique; and `password` creates the password. The function `expand_clique` takes a node, a graph, and a partially-formed clique. It adds the node to the clique, and recursively looks for and adds any other nodes that should be added, finally returning the clique."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 928,
+   "execution_count": 276,
    "id": "88811073-22b2-4378-afa5-9d38462c63b5",
    "metadata": {},
    "outputs": [],
@@ -8911,7 +7685,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 929,
+   "execution_count": 277,
    "id": "0b5f08ac-18e2-4933-9737-cdbc842c5809",
    "metadata": {},
    "outputs": [
@@ -8921,7 +7695,7 @@
        "Puzzle 23.2:   .003 seconds, answer bo,dd,eq,ik,lo,lu,ph,ro,rr,rw,uo,wx,yg ok"
       ]
      },
-     "execution_count": 929,
+     "execution_count": 277,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -8942,7 +7716,7 @@
     "\n",
     "    {BCD}--{A}--{EF}\n",
     "\n",
-    "The call to `expand_cliqe(A, ...)` might return either `{ABCD}` or `{AEF}`, so it might miss the maximum clique. For this case, `expand_cliqe(B, ...)` will indeed always `{ABCD}`. But I'm not quite sure there can't be some more complex configuration where my algorithm fails."
+    "The call to `expand_cliqe(A, ...)` might return either `{ABCD}` or `{AEF}`, so it might miss the maximum clique. For this example, if we missed on `A`, we would still get `{ABCD}` from `B` or `C` or `D`. But I'm not quite sure there can't be some more complex configuration where my algorithm fails."
    ]
   },
   {
@@ -8952,7 +7726,7 @@
    "source": [
     "# [Day 24](https://adventofcode.com/2024/day/24): Crossed Wire\n",
     "\n",
-    "Today we are trying to help the historian to debug a malfunctioning monitoring device, which consistes of some wires and logic gates. Some of the wires have been misrouted. The day's input described the connections in the device. There are two types of inputs: an input wire is described with its name and its bit value: `x00: 1`, and a logic gate is described with the two input wire names, the operation, and the output wire name: `x00 AND y00 -> z00`.\n",
+    "Today we are trying to help the historian to debug a malfunctioning **monitoring device**, which consistes of some wires and logic gates. Some of the wires have been misrouted. The day's input described the connections in the device. There are two types of inputs: an input wire is described with its name and its bit value: `x00: 1`, and a logic gate is described with the two input wire names, the operation, and the output wire name: `x00 AND y00 -> z00`.\n",
     "\n",
     "<img src=\"https://files.mastodon.social/media_attachments/files/113/709/889/001/483/227/small/5803deed6973ab22.jpg\" width=400>\n",
     "\n",
@@ -8961,7 +7735,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 932,
+   "execution_count": 280,
    "id": "47421581-71df-4c72-a62e-c40d0596fdbb",
    "metadata": {},
    "outputs": [
@@ -9012,7 +7786,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 934,
+   "execution_count": 282,
    "id": "43b29260-d912-4cfc-91ce-d303ec1c86df",
    "metadata": {},
    "outputs": [],
@@ -9038,7 +7812,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 936,
+   "execution_count": 284,
    "id": "a9a4780f-6033-452f-b49c-74b97c9e2440",
    "metadata": {},
    "outputs": [],
@@ -9060,7 +7834,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 937,
+   "execution_count": 285,
    "id": "72437439-dddf-4202-9944-36e796800304",
    "metadata": {},
    "outputs": [
@@ -9070,7 +7844,7 @@
        "Puzzle 24.1:   .001 seconds, answer 36035961805936    ok"
       ]
      },
-     "execution_count": 937,
+     "execution_count": 285,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -9103,9 +7877,8 @@
     "\n",
     "I have four ideas of how to proceed, none of them completely compelling:\n",
     "1) Plot the circuit diagram and see if anythng looks funny.\n",
-    "    - Making a nice plot might be tedious, and I'm worried about the ordering of the two input wires to each gate being confusing.\n",
+    "    - Making a nice plot would be hard; I'm worried that wires in a circuit diagram cross each other; that seems hard to do cleanly.\n",
     "2) Examine the structure of the device and look for something that breaks the pattern.\n",
-    "    - For example, calculate the depth, number of transitive inputs, number of transitive outputs, etc. for each gate, and look for broken patterns.\n",
     "    - This might help me, as a detective, uncover the answer, but if I was given another input device I'd have to start all over.\n",
     "3) Choose `x` and `y` numbers as input, run the simulation, and compare the resulting `z` values to the correct answer.\n",
     "    - If I chose random numbers it might take a long time to isolate the faults.\n",
@@ -9114,8 +7887,97 @@
     "4) I know how an adder circuit is conventionally built; if our device is like that, we should be able to see if each bit conforms to the pattern.\n",
     "    - When it doesn't, I can swap wires to make it conform.\n",
     "    - I don't know if this approach will find all faults.\n",
-    "    - It could be that the device is a correct adder, but is built in a non-conventional way.\n",
-    " \n",
+    "    - It could be that the device is a correct adder, but is built in a non-conventional way."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3691add5-cd06-4b74-ac5a-7569a1ccb081",
+   "metadata": {},
+   "source": [
+    "I started with approach (2). A simple thing to try is to look at all the gates that lead directly to the outputs:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 289,
+   "id": "9021ad30-f505-4164-9feb-5af740632182",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{'z45': ('nrv', 'OR', 'jsp'),\n",
+       " 'z44': ('jsg', 'XOR', 'hks'),\n",
+       " 'z43': ('gsk', 'XOR', 'fhk'),\n",
+       " 'z42': ('cng', 'XOR', 'mwt'),\n",
+       " 'z41': ('jhg', 'XOR', 'gfd'),\n",
+       " 'z40': ('nns', 'XOR', 'jbd'),\n",
+       " 'z39': ('vqf', 'XOR', 'fkq'),\n",
+       " 'z38': ('sqj', 'XOR', 'wts'),\n",
+       " 'z37': ('jgw', 'OR', 'rhh'),\n",
+       " 'z36': ('rfq', 'XOR', 'hbh'),\n",
+       " 'z35': ('djt', 'XOR', 'khf'),\n",
+       " 'z34': ('jmv', 'XOR', 'nss'),\n",
+       " 'z33': ('dts', 'XOR', 'wmq'),\n",
+       " 'z32': ('rck', 'XOR', 'ftq'),\n",
+       " 'z31': ('rms', 'XOR', 'sgf'),\n",
+       " 'z30': ('pwp', 'XOR', 'nnn'),\n",
+       " 'z29': ('tsk', 'XOR', 'hvc'),\n",
+       " 'z28': ('msf', 'XOR', 'kdd'),\n",
+       " 'z27': ('tvf', 'XOR', 'cmb'),\n",
+       " 'z26': ('wkb', 'XOR', 'jkr'),\n",
+       " 'z25': ('pfc', 'XOR', 'prp'),\n",
+       " 'z24': ('gww', 'XOR', 'jmf'),\n",
+       " 'z23': ('mcp', 'XOR', 'mkf'),\n",
+       " 'z22': ('wwp', 'XOR', 'bvr'),\n",
+       " 'z21': ('qpm', 'XOR', 'csw'),\n",
+       " 'z20': ('bvw', 'XOR', 'hvn'),\n",
+       " 'z19': ('y19', 'AND', 'x19'),\n",
+       " 'z18': ('qvq', 'XOR', 'hns'),\n",
+       " 'z17': ('wrc', 'XOR', 'hbw'),\n",
+       " 'z16': ('rvn', 'XOR', 'kbq'),\n",
+       " 'z15': ('skh', 'XOR', 'rkt'),\n",
+       " 'z14': ('cgg', 'XOR', 'rhf'),\n",
+       " 'z13': ('jkm', 'XOR', 'dmp'),\n",
+       " 'z12': ('htn', 'XOR', 'dtq'),\n",
+       " 'z11': ('gkc', 'AND', 'qqw'),\n",
+       " 'z10': ('kmr', 'XOR', 'rmb'),\n",
+       " 'z09': ('wpb', 'XOR', 'kbb'),\n",
+       " 'z08': ('rjs', 'XOR', 'tmg'),\n",
+       " 'z07': ('qmb', 'XOR', 'qpc'),\n",
+       " 'z06': ('jtg', 'XOR', 'cfn'),\n",
+       " 'z05': ('whf', 'XOR', 'fds'),\n",
+       " 'z04': ('jvf', 'XOR', 'jth'),\n",
+       " 'z03': ('wvt', 'XOR', 'sbt'),\n",
+       " 'z02': ('rvm', 'XOR', 'vdq'),\n",
+       " 'z01': ('hjp', 'XOR', 'kjs'),\n",
+       " 'z00': ('x00', 'XOR', 'y00')}"
+      ]
+     },
+     "execution_count": 289,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "D = Device(connections)\n",
+    "zs = wires(D, 'z')\n",
+    "{z: D[z] for z in zs}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "aadf7dfc-32a1-4409-9f61-ae08741868ef",
+   "metadata": {},
+   "source": [
+    "Right away I can see three anomalies: \n",
+    "- `z37` has an OR gate instead of an XOR.\n",
+    "- `z11` has an AND gate instead of an XOR.\n",
+    "- `z19` connects directly to the inputs `x19` and `y19`; no other `z` does that (except `z00`, which has no carry bit).\n",
+    "\n",
+    "I'm already 3/8 of the way there! I tried a few other things but didn't make progress, so I decided to go for approach (4).\n",
+    "\n",
     "Here's a picture of a (one-bit) full adder; we have two XOR gates, two AND gates, and one OR gate for every output wire (except for `z00`, which doesn't have a carry bit). \n",
     "![Adder from Wikipedia](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCXZpXA19TudYZz-S51V6WZ_b1HPAbA-uozACxQdnavllWn9oUrVwID5eOmtOhUhFHZZKadar5TY3os2H-Vs4uiCK92wEERCFSOAamOTwOZTQ_q034zdMUhSmxYNihUHWRIRVwLJVoR7Zo1u7-dPL9gysEifyvQqO8AnTvGv9oEAgkxTZMuVyNVN-D/w400-h245/nbit_1.png) \n",
     "\n",
@@ -9124,7 +7986,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 940,
+   "execution_count": 291,
    "id": "3b41a166-d33b-402b-971b-1dc1d33135ec",
    "metadata": {},
    "outputs": [
@@ -9134,7 +7996,7 @@
        "Counter({'AND': 89, 'XOR': 89, 'OR': 44})"
       ]
      },
-     "execution_count": 940,
+     "execution_count": 291,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -9148,14 +8010,14 @@
    "id": "c1f072b2-8c7f-40b2-9712-d0fc0dee62e7",
    "metadata": {},
    "source": [
-    "It does match, so I guess our device is probably implementing the conventional circuit layout. Therefore I'll try approach (4). \n",
+    "It does match, so I guess our device is probably implementing the conventional circuit layout.  \n",
     " \n",
     "The first trouble I ran into was that the two inputs to a gate could be in either order. I will canonicalize this, so that the first input wire is always alphabetically before the second one. The function `canon` enforces this canonicalization. I'll redefine `Device` to use it, and also to cache the **inverse** mapping: from gates to output wires rather than from output wires to gates/bits."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 942,
+   "execution_count": 293,
    "id": "ec8d86d4-8caf-40f2-b516-c7da4acbda19",
    "metadata": {},
    "outputs": [],
@@ -9169,8 +8031,12 @@
     "                case (wire, bit):          # e.g., ('x00', 1)\n",
     "                    self[wire] = bit\n",
     "                case (x, op, y, out):      # e.g., ('y33', 'AND', 'x33', 'bfn')\n",
-    "                    self[out] = canon(x, op, y) # canonicalize order \n",
-    "        self.inverse = {self[w]: w for w in self if self[w] not in (0, 1)} # Inverse mapping\n",
+    "                    self[out] = canon(x, op, y) # canonicalize order\n",
+    "        self.compute_outputs()\n",
+    "        \n",
+    "    def compute_outputs(self):\n",
+    "        \"\"\"Make a mapping {gate: output wire name}.\"\"\"\n",
+    "        self.outputs = {self[w]: w for w in self if self[w] not in (0, 1)} \n",
     "                    \n",
     "def canon(x, op, y) -> Tuple: \n",
     "    \"\"\"The canonical ordering of the two input wires (and the operator).\"\"\"\n",
@@ -9187,46 +8053,45 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 944,
+   "execution_count": 295,
    "id": "7ed8f8e6-c3e1-4c22-b812-e1a201afec3d",
    "metadata": {},
    "outputs": [],
    "source": [
-    "def find_swaps(device):\n",
+    "def find_swaps(device) -> Iterable[str]:\n",
     "    \"\"\"For each bit position in the inputs, x and y, look forward for the\n",
     "    XOR and AND gates they participate in, then look backwards from the \n",
     "    corresponding z output, and see where they fail to match up,\n",
     "    and swap wires accordingly, yielding each swapped wire.\"\"\"\n",
     "    \n",
-    "    def wire(x, op, y): return device.inverse.get(canon(x, op, y), None)\n",
+    "    def output(x, op, y): return device.outputs.get(canon(x, op, y), None)\n",
     "        \n",
     "    for i in range(len(wires(device, 'x'))):\n",
     "        x, y, z = [f'{v}{i:02d}' for v in 'xyz']\n",
     "        if x == 'x00':\n",
-    "            carry = wire(x, 'AND', y)\n",
+    "            carry = output(x, 'AND', y)\n",
     "        else:\n",
-    "            a, b = carry, wire(x, 'XOR', y)\n",
-    "            if not wire(a, 'XOR', b):\n",
+    "            a, b = carry, output(x, 'XOR', y)\n",
+    "            if not output(a, 'XOR', b):\n",
     "                a2, op, b2, = device[z] # Look backwards from z to see if they hook up\n",
     "                once = [w for w in (a, b, a2, b2) if [a, b, a2, b2].count(w) == 1]\n",
     "                if len(once) == 2: # Wires that appear once in the two gates; they don't connect properly\n",
     "                  yield from swap(*once, device)\n",
-    "            elif wire(a, 'XOR', b) != z:\n",
-    "                yield from swap(z, wire(a, 'XOR', b), device)\n",
-    "            carry = wire(carry, 'AND', wire(x, 'XOR', y)) # The carry gets propagated through two gates\n",
-    "            carry = wire(carry, 'OR',  wire(x, 'AND', y))\n",
+    "            elif output(a, 'XOR', b) != z:\n",
+    "                yield from swap(z, output(a, 'XOR', b), device)\n",
+    "            carry = output(carry, 'AND', output(x, 'XOR', y)) # The carry gets propagated through two gates\n",
+    "            carry = output(carry, 'OR',  output(x, 'AND', y))\n",
     "\n",
     "def swap(a: str, b: str, device: dict) -> Set[str]:\n",
-    "    \"\"\"Swap wires `a` and `b` in device (and also update the inverse mapping).\"\"\"\n",
-    "    inv = device.inverse\n",
+    "    \"\"\"Swap wires `a` and `b` in device.\"\"\"\n",
     "    device[a], device[b] = device[b], device[a]\n",
-    "    inv[device[a]], inv[device[b]] = inv[device[b]], inv[device[a]]\n",
+    "    device.compute_outputs() # Recompute outputs after this swap\n",
     "    return a, b"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 945,
+   "execution_count": 296,
    "id": "e9b87c38-f67c-4948-9af6-251021747e9d",
    "metadata": {},
    "outputs": [
@@ -9236,7 +8101,7 @@
        "Puzzle 24.2:   .000 seconds, answer jqf,mdd,skh,wpd,wts,z11,z19,z37 ok"
       ]
      },
-     "execution_count": 945,
+     "execution_count": 296,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -9253,14 +8118,14 @@
    "source": [
     "# [Day 25](https://adventofcode.com/2024/day/25): Code Chronicle\n",
     "\n",
-    "We're trying to get into the Chief Historian's office, but the door is locked. We have the schematics of all the locks and keys on the floor we're on, and we need to see which key could fit which lock. A lock is described with 5 columns of different length growing down from the top, and a key has five columns growing up from the bottom. A key and a lock are a possible fit if none of the five lines overlap; that is, since the lock cylinder has height 7 units, it is a possible fit if none of the five columns has more than 7 total `'#'` marks for the lock and the key combined.\n",
+    "We're trying to get into the Chief Historian's office, but the door is locked. We have the schematics of all the **locks** and **keys** on the floor we're on, and we need to see which key could fit which lock. A lock schematic has 5 columns of different length growing down from the top, and a key schematic has five columns growing up from the bottom. A key and a lock are a possible fit if none of the five lines overlap; that is, since the lock cylinder has a height of 7 units, it is a possible fit if none of the five columns has more than 7 total `'#'` marks for the lock and the key combined.\n",
     "\n",
-    "We'll parse the schematics into paragraphs, where each one is a list of lines."
+    "We'll parse the schematics into paragraphs, where each paragraph is a list of lines."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 947,
+   "execution_count": 298,
    "id": "f5971853-7139-4f17-bdc5-6c51e12a928d",
    "metadata": {},
    "outputs": [
@@ -9306,62 +8171,61 @@
    "source": [
     "### Part 1: How many unique lock/key pairs fit together without overlapping in any column?\n",
     "\n",
-    "First we separate the schematics into locks and keys, transforming each one into a list of column heights. To begin with, each schematic is a list of rows. The function `heights` takes the transpose, `T(schematic)`, to get a list of columns, then uses `count` to count the number of `'#'` characters in each column. For example, the first lock is:\n",
+    "This looks pretty easy:\n",
+    "- The function `count_fits` will compute the answer. First it separates the schematics into locks and keys, transforming each one into a list of column heights. Then it counts how many key/lock  combinations fit, trying every possibility.\n",
+    "- The function `column_heights` takes a schematic, which is a list of rows, and applies the transpose, `T(schematic)`, to get a list of columns. Then it uses `count` to count the number of `'#'` characters in each column.\n",
+    "- The function `can_fit` takes takes two lists of column counts and determines if any column has more than 7 total `'#'` characters.\n",
+    "\n",
+    "For example, the first lock is:\n",
     "\n",
     "     ['#####', '####.', '####.', '####.', '##.#.', '#....', '.....']\n",
     "\n",
-    "We transpose that to get a list of columns, and count the number of `'#'` characters in each column:\n",
+    "We transpose that to get a list of columns, \n",
+    "\n",
+    "     ('######.', '#####..', '####...', '#####..', '#......')\n",
+    "\n",
+    "and count the number of `'#'` characters in each column:\n",
     "\n",
     "     [6, 5, 4, 5, 1]\n",
     "\n",
-    "Then for each lock/key pair, we see if they can fit by checking that all columns have no more than 7 total `'#'` characters."
+    "Here is the code:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 949,
+   "execution_count": 300,
    "id": "5302ac58-91fc-475a-83d9-cea91457df3b",
    "metadata": {},
    "outputs": [],
    "source": [
     "def count_fits(schematics) -> List:\n",
     "    \"\"\"Try all key/lock combinations and count how many fit each other.\"\"\"\n",
-    "    locks = [heights(s) for s in schematics if s[0] == '#####']\n",
-    "    keys  = [heights(s) for s in schematics if s[0] != '#####']\n",
+    "    locks = [column_heights(s) for s in schematics if s[0] == '#####']\n",
+    "    keys  = [column_heights(s) for s in schematics if s[0] != '#####']\n",
     "    return quantify(can_fit(key, lock) for lock in locks for key in keys)\n",
     "    \n",
+    "def column_heights(schematic) -> List[int]:\n",
+    "    \"\"\"A counter of {column_number: (number of '#' in that column)}.\"\"\"\n",
+    "    return [column.count('#') for column in T(schematic)] # Remember, `T` is transpose\n",
+    "    \n",
     "def can_fit(key: Ints, lock: Ints): \n",
     "    \"\"\"The key can fit the lock if the sum of the '#' count in each column is <= 7.\"\"\"\n",
-    "    return all(lock[c] + key[c] <= 7 for c in range(5))\n",
-    "\n",
-    "def heights(schematic) -> List[int]:\n",
-    "    \"\"\"A counter of {column_number: (number of '#' in that column)}.\"\"\"\n",
-    "    return [column.count('#') for column in T(schematic)] # Remember, `T` is transpose"
+    "    return all(lock[c] + key[c] <= 7 for c in range(5))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 950,
-   "id": "c415f5c1-76c3-486c-9075-c46a5a8c5bcb",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "assert heights(['#####', '####.', '####.', '####.', '##.#.', '#....', '.....']) == [6, 5, 4, 5, 1]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 951,
+   "execution_count": 301,
    "id": "89c28b74-ed31-4bb5-b463-7177952a95ae",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Puzzle 25.1:   .022 seconds, answer 3196              ok"
+       "Puzzle 25.1:   .021 seconds, answer 3196              ok"
       ]
      },
-     "execution_count": 951,
+     "execution_count": 301,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -9376,9 +8240,9 @@
    "id": "ce1c8e04-5297-4798-969d-3cc9210bfd9a",
    "metadata": {},
    "source": [
-    "And with that, we're done! \n",
+    "And with that, **we're done!** \n",
     "\n",
-    "Thanks, [Eric Wastl](https://adventofcode.com/2024/about)!\n",
+    "Thanks, [**Eric Wastl**](https://adventofcode.com/2024/about), and congratulations for ten years of AoC!\n",
     "\n",
     "<img src=\"https://files.mastodon.social/media_attachments/files/113/714/790/660/920/471/small/c34a34c48bad3d94.jpg\" width=400>"
    ]
@@ -9390,14 +8254,14 @@
    "source": [
     "# Summary\n",
     "\n",
-    "Here are all the puzzle answers and timings. I got all the puzzles right! And I did it before midnight on December 25th, a rarity for me. \n",
+    "Here are all the puzzle answers and timings. I got all the puzzles right! And I did it before midnight (my time) on December 25th, a rarity for me. \n",
     "\n",
-    "The median run time is under 10 milliseconds, with 4 puzzles taking over a second. I didn't count the time that `parse` takes, but that is less than a millisecond per day."
+    "The median run time is about 5 milliseconds, with 4 puzzles taking over a second. I didn't count the time that `parse` takes, but that is less than a millisecond per day."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 954,
+   "execution_count": 304,
    "id": "34813fc9-a000-4cd8-88ae-692851b3242c",
    "metadata": {},
    "outputs": [
@@ -9411,53 +8275,53 @@
       "Puzzle  2.2:   .002 seconds, answer 328               ok\n",
       "Puzzle  3.1:   .001 seconds, answer 156388521         ok\n",
       "Puzzle  3.2:   .000 seconds, answer 75920122          ok\n",
-      "Puzzle  4.1:   .022 seconds, answer 2401              ok\n",
+      "Puzzle  4.1:   .020 seconds, answer 2401              ok\n",
       "Puzzle  4.2:   .016 seconds, answer 1822              ok\n",
       "Puzzle  5.1:   .001 seconds, answer 5762              ok\n",
       "Puzzle  5.2:   .001 seconds, answer 4130              ok\n",
-      "Puzzle  6.1:   .002 seconds, answer 5329              ok\n",
-      "Puzzle  6.2:  1.976 seconds, answer 2162              ok\n",
+      "Puzzle  6.1:   .001 seconds, answer 5329              ok\n",
+      "Puzzle  6.2:  1.998 seconds, answer 2162              ok\n",
       "Puzzle  7.1:   .014 seconds, answer 1985268524462     ok\n",
-      "Puzzle  7.2:   .593 seconds, answer 150077710195188   ok\n",
-      "Puzzle  8.1:   .003 seconds, answer 220               ok\n",
+      "Puzzle  7.2:   .606 seconds, answer 150077710195188   ok\n",
+      "Puzzle  8.1:   .002 seconds, answer 220               ok\n",
       "Puzzle  8.2:   .003 seconds, answer 813               ok\n",
       "Puzzle  9.1:   .020 seconds, answer 6332189866718     ok\n",
-      "Puzzle  9.2:  2.748 seconds, answer 6353648390778     ok\n",
+      "Puzzle  9.2:  2.428 seconds, answer 6353648390778     ok\n",
       "Puzzle 10.1:   .005 seconds, answer 744               ok\n",
       "Puzzle 10.2:   .006 seconds, answer 1651              ok\n",
-      "Puzzle 11.1:   .002 seconds, answer 194482            ok\n",
-      "Puzzle 11.2:   .055 seconds, answer 232454623677743   ok\n",
+      "Puzzle 11.1:   .001 seconds, answer 194482            ok\n",
+      "Puzzle 11.2:   .061 seconds, answer 232454623677743   ok\n",
       "Puzzle 12.1:   .030 seconds, answer 1402544           ok\n",
-      "Puzzle 12.2:   .042 seconds, answer 862486            ok\n",
+      "Puzzle 12.2:   .061 seconds, answer 862486            ok\n",
       "Puzzle 13.1:   .000 seconds, answer 29598             ok\n",
       "Puzzle 13.2:   .000 seconds, answer 93217456941970    ok\n",
       "Puzzle 14.1:   .000 seconds, answer 216027840         ok\n",
-      "Puzzle 14.2:  1.833 seconds, answer 6876              ok\n",
+      "Puzzle 14.2:  1.874 seconds, answer 6876              ok\n",
       "Puzzle 15.1:   .029 seconds, answer 1563092           ok\n",
       "Puzzle 15.2:   .042 seconds, answer 1582688           ok\n",
-      "Puzzle 16.1:   .139 seconds, answer 103512            ok\n",
-      "Puzzle 16.2:   .985 seconds, answer 554               ok\n",
+      "Puzzle 16.1:   .146 seconds, answer 103512            ok\n",
+      "Puzzle 16.2:   .863 seconds, answer 554               ok\n",
       "Puzzle 17.1:   .000 seconds, answer 2,1,0,1,7,2,5,0,3 ok\n",
       "Puzzle 17.2:   .004 seconds, answer 267265166222235   ok\n",
       "Puzzle 18.1:   .014 seconds, answer 344               ok\n",
-      "Puzzle 18.2:   .032 seconds, answer 46,18             ok\n",
-      "Puzzle 19.1:   .002 seconds, answer 242               ok\n",
-      "Puzzle 19.2:   .185 seconds, answer 595975512785325   ok\n",
+      "Puzzle 18.2:   .033 seconds, answer 46,18             ok\n",
+      "Puzzle 19.1:   .004 seconds, answer 242               ok\n",
+      "Puzzle 19.2:   .189 seconds, answer 595975512785325   ok\n",
       "Puzzle 20.1:   .023 seconds, answer 1343              ok\n",
-      "Puzzle 20.2:   .757 seconds, answer 982891            ok\n",
-      "Puzzle 21.1:   .002 seconds, answer 205160            ok\n",
-      "Puzzle 21.2:   .008 seconds, answer 252473394928452   ok\n",
-      "Puzzle 22.1:   .305 seconds, answer 14273043166       ok\n",
-      "Puzzle 22.2:  1.295 seconds, answer 1667              ok\n",
+      "Puzzle 20.2:   .773 seconds, answer 982891            ok\n",
+      "Puzzle 21.1:   .000 seconds, answer 205160            ok\n",
+      "Puzzle 21.2:   .004 seconds, answer 252473394928452   ok\n",
+      "Puzzle 22.1:   .325 seconds, answer 14273043166       ok\n",
+      "Puzzle 22.2:  1.285 seconds, answer 1667              ok\n",
       "Puzzle 23.1:   .001 seconds, answer 1170              ok\n",
       "Puzzle 23.2:   .003 seconds, answer bo,dd,eq,ik,lo,lu,ph,ro,rr,rw,uo,wx,yg ok\n",
       "Puzzle 24.1:   .001 seconds, answer 36035961805936    ok\n",
       "Puzzle 24.2:   .000 seconds, answer jqf,mdd,skh,wpd,wts,z11,z19,z37 ok\n",
-      "Puzzle 25.1:   .022 seconds, answer 3196              ok\n",
+      "Puzzle 25.1:   .021 seconds, answer 3196              ok\n",
       "\n",
       "Correct: 49/49\n",
       "\n",
-      "Time in seconds: 0.006 median, 0.229 mean, 11.227 total.\n"
+      "Time in seconds: 0.005 median, 0.223 mean, 10.914 total.\n"
      ]
     }
    ],
diff --git a/ipynb/AdventUtils.ipynb b/ipynb/AdventUtils.ipynb
index 61194a5..a00cfd1 100644
--- a/ipynb/AdventUtils.ipynb
+++ b/ipynb/AdventUtils.ipynb
@@ -420,11 +420,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 154,
    "metadata": {},
    "outputs": [],
    "source": [
     "Point  = Tuple[int, ...]      # Type for points\n",
+    "Point2D = Tuple[int, int]     # Type for 2-dimensional point\n",
     "Vector = Point                # E.g., (1, 0) can be a point, or can be a direction, a Vector\n",
     "Zero   = (0, 0)\n",
     "\n",
@@ -444,43 +445,40 @@
     "def Ys(points) -> Tuple[int]: \"Y coordinates of a collection of points\"; return mapt(Y_, points)\n",
     "def Zs(points) -> Tuple[int]: \"X coordinates of a collection of points\"; return mapt(Z_, points)\n",
     "\n",
-    "def add(p: Point, q: Point) -> Point:  \"Add points\";      return mapt(operator.add, p, q)\n",
-    "def sub(p: Point, q: Point) -> Point:  \"Subtract points\"; return mapt(operator.sub, p, q)\n",
-    "def neg(p: Point)           -> Vector: \"Negate a point\";  return mapt(operator.neg, p)\n",
-    "def mul(p: Point, k: float) -> Vector: \"Scalar multiply\"; return tuple(k * c for c in p)\n",
+    "## I define point arithmetic for general points and separate versions for 2D points,\n",
+    "## because profiling showed the 2D versions are significantly faster\n",
     "\n",
-    "def distance(p: Point, q: Point) -> float:\n",
-    "    \"\"\"Euclidean (L2) distance between two points.\"\"\"\n",
-    "    d = sum((pi - qi) ** 2 for pi, qi in zip(p, q)) ** 0.5\n",
-    "    return int(d) if d.is_integer() else d\n",
+    "def add3(p: Point, q: Point) -> Point:  \"Add points\";      return mapt(operator.add, p, q)\n",
+    "def sub3(p: Point, q: Point) -> Point:  \"Subtract points\"; return mapt(operator.sub, p, q)\n",
+    "def mul3(p: Point, k: float) -> Vector: \"Scalar multiply\"; return tuple(k * c for c in p)\n",
+    "def neg(p: Point2D)             -> Vector:  \"Negate a 2D Point\";  return mapt(operator.neg, p)\n",
+    "\n",
+    "def add(p: Point2D, q: Point2D) -> Point2D: \"Add 2D Points\";      return (p[0] + q[0], p[1] + q[1])\n",
+    "def sub(p: Point2D, q: Point2D) -> Point2D: \"Subtract 2D Points\"; return (p[0] - q[0], p[1] - q[1])\n",
+    "def mul(p: Point2D, k: float)   -> Point2D: \"Scalar multiply\";    return (p[0] * k, p[1] * k)\n",
+    "def neg(p: Point2D)             -> Vector:  \"Negate a 2D Point\";  return (-p[0], -p[1])\n",
     "\n",
     "def slide(points: Set[Point], delta: Vector) -> Set[Point]: \n",
     "    \"\"\"Slide all the points in the set of points by the amount delta.\"\"\"\n",
     "    return {add(p, delta) for p in points}\n",
     "\n",
-    "def make_turn(facing:Vector, turn:str) -> Vector:\n",
+    "def make_turn(facing: Vector, turn: str) -> Vector:\n",
     "    \"\"\"Turn 90 degrees left or right. `turn` can be 'L' or 'Left' or 'R' or 'Right' or lowercase.\"\"\"\n",
     "    (x, y) = facing\n",
     "    return (y, -x) if turn[0] in ('L', 'l') else (-y, x)\n",
     "\n",
-    "# Profiling found that `add` and `taxi_distance` were speed bottlenecks; \n",
-    "# I define below versions that are specialized for 2D points only.\n",
-    "\n",
-    "def add2(p: Point, q: Point) -> Point: \n",
-    "    \"\"\"Specialized version of point addition for 2D Points only. Faster.\"\"\"\n",
-    "    return (p[0] + q[0], p[1] + q[1])\n",
-    "\n",
-    "def sub2(p: Point, q: Point) -> Point: \n",
-    "    \"\"\"Specialized version of point subtraction for 2D Points only. Faster.\"\"\"\n",
-    "    return (p[0] - q[0], p[1] - q[1])\n",
-    "\n",
-    "def taxi_distance(p: Point, q: Point) -> int:\n",
-    "    \"\"\"Manhattan (L1) distance between two 2D Points.\"\"\"\n",
-    "    return abs(p[0] - q[0]) + abs(p[1] - q[1])\n",
-    "\n",
-    "def distance_squared(p: Point, q: Point) -> float:\n",
+    "def distance(p: Point2D, q: Point2D) -> float:\n",
+    "    \"\"\"Euclidean (L2) distance between two points.\"\"\"\n",
+    "    d = sum((pi - qi) ** 2 for pi, qi in zip(p, q)) ** 0.5\n",
+    "    return int(d) if d.is_integer() else d\n",
+    "    \n",
+    "def distance_squared(p: Point2D, q: Point2D) -> float:\n",
     "    \"\"\"Square of the Euclidean (L2) distance between two 2D points.\"\"\"\n",
-    "    return (p[0] - q[0]) ** 2 + (p[1] - q[1]) ** 2"
+    "    return (p[0] - q[0]) ** 2 + (p[1] - q[1]) ** 2\n",
+    "    \n",
+    "def taxi_distance(p: Point2D, q: Point2D) -> int:\n",
+    "    \"\"\"Manhattan (L1) distance between two 2D Points.\"\"\"\n",
+    "    return abs(p[0] - q[0]) + abs(p[1] - q[1])"
    ]
   },
   {
@@ -545,15 +543,15 @@
     "    def follow_line(self, start: Point, direction: Vector) -> Iterable[Point]:\n",
     "        while self.in_range(start):\n",
     "            yield start\n",
-    "            start = add2(start, direction)\n",
+    "            start = add(start, direction)\n",
     "\n",
     "    def copy(self): \n",
     "        return Grid(self, directions=self.directions, skip=self.skip, default=self.default)\n",
     "    \n",
     "    def neighbors(self, point) -> List[Point]:\n",
     "        \"\"\"Points on the grid that neighbor `point`.\"\"\"\n",
-    "        return [add2(point, Δ) for Δ in self.directions \n",
-    "                if (add2(point, Δ) in self) \n",
+    "        return [add(point, Δ) for Δ in self.directions \n",
+    "                if (add(point, Δ) in self) \n",
     "                or (self.default not in (KeyError, None))]\n",
     "    \n",
     "    def neighbor_contents(self, point) -> Iterable:\n",
@@ -790,6 +788,33 @@
     "        self[attr] = value"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def get_size(obj, seen: Optional[Set[int]] = None) -> int:\n",
+    "  \"\"\"Recursively finds size of objects.\"\"\"\n",
+    "  seen = set() if seen is None else seen\n",
+    "\n",
+    "  if id(obj) in seen: return 0  # to handle self-referential objects\n",
+    "  seen.add(id(obj))\n",
+    "\n",
+    "  size = sys.getsizeof(obj, 0) # pypy3 always returns default (necessary)\n",
+    "  if isinstance(obj, dict):\n",
+    "    size += sum(getSize(v, seen) + getSize(k, seen) for k, v in obj.items())\n",
+    "  elif hasattr(obj, '__dict__'):\n",
+    "    size += getSize(obj.__dict__, seen)\n",
+    "  elif hasattr(obj, '__slots__'): # in case slots are in use\n",
+    "    slotList = [getattr(C, \"__slots__\", []) for C in obj.__class__.__mro__]\n",
+    "    slotList = [[slot] if isinstance(slot, str) else slot for slot in slotList]\n",
+    "    size += sum(getSize(getattr(obj, a, None), seen) for slot in slotList for a in slot)\n",
+    "  elif hasattr(obj, '__iter__') and not isinstance(obj, (str, bytes, bytearray)):\n",
+    "    size += sum(getSize(i, seen) for i in obj)\n",
+    "  return size"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},