diff --git a/ipynb/Advent-2024.ipynb b/ipynb/Advent-2024.ipynb
index ff90cc6..eacf85b 100644
--- a/ipynb/Advent-2024.ipynb
+++ b/ipynb/Advent-2024.ipynb
@@ -136,7 +136,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  1.1:   .0002 seconds, answer 1830467           ok"
+       "Puzzle  1.1:   .000 seconds, answer 1830467           ok"
       ]
      },
      "execution_count": 8,
@@ -181,7 +181,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  1.2:   .0001 seconds, answer 26674158          ok"
+       "Puzzle  1.2:   .000 seconds, answer 26674158          ok"
       ]
      },
      "execution_count": 11,
@@ -284,7 +284,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  2.1:   .0004 seconds, answer 257               ok"
+       "Puzzle  2.1:   .000 seconds, answer 257               ok"
       ]
      },
      "execution_count": 16,
@@ -334,7 +334,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  2.2:   .0022 seconds, answer 328               ok"
+       "Puzzle  2.2:   .002 seconds, answer 328               ok"
       ]
      },
      "execution_count": 19,
@@ -419,7 +419,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  3.1:   .0006 seconds, answer 156388521         ok"
+       "Puzzle  3.1:   .001 seconds, answer 156388521         ok"
       ]
      },
      "execution_count": 24,
@@ -463,7 +463,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  3.2:   .0004 seconds, answer 75920122          ok"
+       "Puzzle  3.2:   .000 seconds, answer 75920122          ok"
       ]
      },
      "execution_count": 27,
@@ -553,7 +553,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  4.1:   .0331 seconds, answer 2401              ok"
+       "Puzzle  4.1:   .033 seconds, answer 2401              ok"
       ]
      },
      "execution_count": 32,
@@ -608,7 +608,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  4.2:   .0273 seconds, answer 1822              ok"
+       "Puzzle  4.2:   .027 seconds, answer 1822              ok"
       ]
      },
      "execution_count": 35,
@@ -738,7 +738,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  5.1:   .0007 seconds, answer 5762              ok"
+       "Puzzle  5.1:   .001 seconds, answer 5762              ok"
       ]
      },
      "execution_count": 41,
@@ -823,7 +823,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  5.2:   .0008 seconds, answer 4130              ok"
+       "Puzzle  5.2:   .001 seconds, answer 4130              ok"
       ]
      },
      "execution_count": 46,
@@ -923,7 +923,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  6.1:   .0016 seconds, answer 5329              ok"
+       "Puzzle  6.1:   .002 seconds, answer 5329              ok"
       ]
      },
      "execution_count": 52,
@@ -993,7 +993,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  6.2:  1.9960 seconds, answer 2162              ok"
+       "Puzzle  6.2:  1.968 seconds, answer 2162              ok"
       ]
      },
      "execution_count": 55,
@@ -1139,7 +1139,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  7.1:   .0137 seconds, answer 1985268524462     ok"
+       "Puzzle  7.1:   .014 seconds, answer 1985268524462     ok"
       ]
      },
      "execution_count": 64,
@@ -1181,7 +1181,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  7.2:   .8158 seconds, answer 150077710195188   ok"
+       "Puzzle  7.2:   .801 seconds, answer 150077710195188   ok"
       ]
      },
      "execution_count": 67,
@@ -1229,7 +1229,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  7.2:   .6577 seconds, answer 150077710195188   ok"
+       "Puzzle  7.2:   .656 seconds, answer 150077710195188   ok"
       ]
      },
      "execution_count": 70,
@@ -1323,7 +1323,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  8.1:   .0029 seconds, answer 220               ok"
+       "Puzzle  8.1:   .003 seconds, answer 220               ok"
       ]
      },
      "execution_count": 75,
@@ -1378,7 +1378,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  8.1:   .0027 seconds, answer 220               ok"
+       "Puzzle  8.1:   .003 seconds, answer 220               ok"
       ]
      },
      "execution_count": 78,
@@ -1400,7 +1400,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  8.2:   .0030 seconds, answer 813               ok"
+       "Puzzle  8.2:   .003 seconds, answer 813               ok"
       ]
      },
      "execution_count": 79,
@@ -1513,7 +1513,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  9.1:   .0202 seconds, answer 6332189866718     ok"
+       "Puzzle  9.1:   .020 seconds, answer 6332189866718     ok"
       ]
      },
      "execution_count": 85,
@@ -1593,7 +1593,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  9.2:  2.7791 seconds, answer 6353648390778     ok"
+       "Puzzle  9.2:  2.731 seconds, answer 6353648390778     ok"
       ]
      },
      "execution_count": 88,
@@ -1702,7 +1702,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 10.1:   .0047 seconds, answer 744               ok"
+       "Puzzle 10.1:   .005 seconds, answer 744               ok"
       ]
      },
      "execution_count": 94,
@@ -1753,7 +1753,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 10.2:   .0062 seconds, answer 1651              ok"
+       "Puzzle 10.2:   .006 seconds, answer 1651              ok"
       ]
      },
      "execution_count": 97,
@@ -1895,7 +1895,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 11.1:   .0660 seconds, answer 194482            ok"
+       "Puzzle 11.1:   .068 seconds, answer 194482            ok"
       ]
      },
      "execution_count": 104,
@@ -1956,7 +1956,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 11.1:   .0015 seconds, answer 194482            ok"
+       "Puzzle 11.1:   .002 seconds, answer 194482            ok"
       ]
      },
      "execution_count": 108,
@@ -1978,7 +1978,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 11.2:   .0596 seconds, answer 232454623677743   ok"
+       "Puzzle 11.2:   .060 seconds, answer 232454623677743   ok"
       ]
      },
      "execution_count": 109,
@@ -2110,7 +2110,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 12.1:   .0332 seconds, answer 1402544           ok"
+       "Puzzle 12.1:   .033 seconds, answer 1402544           ok"
       ]
      },
      "execution_count": 117,
@@ -2183,7 +2183,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 12.1:   .0501 seconds, answer 1402544           ok"
+       "Puzzle 12.1:   .051 seconds, answer 1402544           ok"
       ]
      },
      "execution_count": 120,
@@ -2205,7 +2205,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 12.2:   .0423 seconds, answer 862486            ok"
+       "Puzzle 12.2:   .042 seconds, answer 862486            ok"
       ]
      },
      "execution_count": 121,
@@ -2325,7 +2325,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 13.1:   .0098 seconds, answer 29598             ok"
+       "Puzzle 13.1:   .010 seconds, answer 29598             ok"
       ]
      },
      "execution_count": 126,
@@ -2447,7 +2447,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 13.2:   .0004 seconds, answer 93217456941970    ok"
+       "Puzzle 13.2:   .000 seconds, answer 93217456941970    ok"
       ]
      },
      "execution_count": 133,
@@ -2477,7 +2477,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 13.1:   .0002 seconds, answer 29598             ok"
+       "Puzzle 13.1:   .000 seconds, answer 29598             ok"
       ]
      },
      "execution_count": 135,
@@ -2582,7 +2582,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 14.1:   .0001 seconds, answer 216027840         ok"
+       "Puzzle 14.1:   .000 seconds, answer 216027840         ok"
       ]
      },
      "execution_count": 140,
@@ -2837,42 +2837,42 @@
        "</style>\n",
        "\n",
        "<div class=\"animation\">\n",
-       "  <img id=\"_anim_img94aebc698f514824b456d60045f1f0fa\">\n",
+       "  <img id=\"_anim_img48c518432d5b41ef99bf29888413d888\">\n",
        "  <div class=\"anim-controls\">\n",
-       "    <input id=\"_anim_slider94aebc698f514824b456d60045f1f0fa\" type=\"range\" class=\"anim-slider\"\n",
+       "    <input id=\"_anim_slider48c518432d5b41ef99bf29888413d888\" type=\"range\" class=\"anim-slider\"\n",
        "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
-       "           oninput=\"anim94aebc698f514824b456d60045f1f0fa.set_frame(parseInt(this.value));\">\n",
+       "           oninput=\"anim48c518432d5b41ef99bf29888413d888.set_frame(parseInt(this.value));\">\n",
        "    <div class=\"anim-buttons\">\n",
-       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anim94aebc698f514824b456d60045f1f0fa.slower()\">\n",
+       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anim48c518432d5b41ef99bf29888413d888.slower()\">\n",
        "          <i class=\"fa fa-minus\"></i></button>\n",
-       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anim94aebc698f514824b456d60045f1f0fa.first_frame()\">\n",
+       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anim48c518432d5b41ef99bf29888413d888.first_frame()\">\n",
        "        <i class=\"fa fa-fast-backward\"></i></button>\n",
-       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anim94aebc698f514824b456d60045f1f0fa.previous_frame()\">\n",
+       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anim48c518432d5b41ef99bf29888413d888.previous_frame()\">\n",
        "          <i class=\"fa fa-step-backward\"></i></button>\n",
-       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anim94aebc698f514824b456d60045f1f0fa.reverse_animation()\">\n",
+       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anim48c518432d5b41ef99bf29888413d888.reverse_animation()\">\n",
        "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
-       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anim94aebc698f514824b456d60045f1f0fa.pause_animation()\">\n",
+       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anim48c518432d5b41ef99bf29888413d888.pause_animation()\">\n",
        "          <i class=\"fa fa-pause\"></i></button>\n",
-       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anim94aebc698f514824b456d60045f1f0fa.play_animation()\">\n",
+       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anim48c518432d5b41ef99bf29888413d888.play_animation()\">\n",
        "          <i class=\"fa fa-play\"></i></button>\n",
-       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anim94aebc698f514824b456d60045f1f0fa.next_frame()\">\n",
+       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anim48c518432d5b41ef99bf29888413d888.next_frame()\">\n",
        "          <i class=\"fa fa-step-forward\"></i></button>\n",
-       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anim94aebc698f514824b456d60045f1f0fa.last_frame()\">\n",
+       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anim48c518432d5b41ef99bf29888413d888.last_frame()\">\n",
        "          <i class=\"fa fa-fast-forward\"></i></button>\n",
-       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anim94aebc698f514824b456d60045f1f0fa.faster()\">\n",
+       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anim48c518432d5b41ef99bf29888413d888.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_select94aebc698f514824b456d60045f1f0fa\"\n",
+       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select48c518432d5b41ef99bf29888413d888\"\n",
        "          class=\"anim-state\">\n",
-       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_94aebc698f514824b456d60045f1f0fa\"\n",
+       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_48c518432d5b41ef99bf29888413d888\"\n",
        "             >\n",
-       "      <label for=\"_anim_radio1_94aebc698f514824b456d60045f1f0fa\">Once</label>\n",
-       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_94aebc698f514824b456d60045f1f0fa\"\n",
+       "      <label for=\"_anim_radio1_48c518432d5b41ef99bf29888413d888\">Once</label>\n",
+       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_48c518432d5b41ef99bf29888413d888\"\n",
        "             checked>\n",
-       "      <label for=\"_anim_radio2_94aebc698f514824b456d60045f1f0fa\">Loop</label>\n",
-       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_94aebc698f514824b456d60045f1f0fa\"\n",
+       "      <label for=\"_anim_radio2_48c518432d5b41ef99bf29888413d888\">Loop</label>\n",
+       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_48c518432d5b41ef99bf29888413d888\"\n",
        "             >\n",
-       "      <label for=\"_anim_radio3_94aebc698f514824b456d60045f1f0fa\">Reflect</label>\n",
+       "      <label for=\"_anim_radio3_48c518432d5b41ef99bf29888413d888\">Reflect</label>\n",
        "    </form>\n",
        "  </div>\n",
        "</div>\n",
@@ -2882,9 +2882,9 @@
        "  /* Instantiate the Animation class. */\n",
        "  /* The IDs given should match those used in the template above. */\n",
        "  (function() {\n",
-       "    var img_id = \"_anim_img94aebc698f514824b456d60045f1f0fa\";\n",
-       "    var slider_id = \"_anim_slider94aebc698f514824b456d60045f1f0fa\";\n",
-       "    var loop_select_id = \"_anim_loop_select94aebc698f514824b456d60045f1f0fa\";\n",
+       "    var img_id = \"_anim_img48c518432d5b41ef99bf29888413d888\";\n",
+       "    var slider_id = \"_anim_slider48c518432d5b41ef99bf29888413d888\";\n",
+       "    var loop_select_id = \"_anim_loop_select48c518432d5b41ef99bf29888413d888\";\n",
        "    var frames = new Array(3);\n",
        "    \n",
        "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA8AAAALQCAYAAABfdxm0AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
@@ -5656,14 +5656,14 @@
        "    /* set a timeout to make sure all the above elements are created before\n",
        "       the object is initialized. */\n",
        "    setTimeout(function() {\n",
-       "        anim94aebc698f514824b456d60045f1f0fa = new Animation(frames, img_id, slider_id, 200.0,\n",
+       "        anim48c518432d5b41ef99bf29888413d888 = 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 0x1398ae5a0>"
+       "<matplotlib.animation.FuncAnimation at 0x16ace4440>"
       ]
      },
      "execution_count": 144,
@@ -5896,42 +5896,42 @@
        "</style>\n",
        "\n",
        "<div class=\"animation\">\n",
-       "  <img id=\"_anim_imge1d73e0327fa420190c43c3033a2c763\">\n",
+       "  <img id=\"_anim_img75c15803e4bc421ab6d6396a5ebe956b\">\n",
        "  <div class=\"anim-controls\">\n",
-       "    <input id=\"_anim_slidere1d73e0327fa420190c43c3033a2c763\" type=\"range\" class=\"anim-slider\"\n",
+       "    <input id=\"_anim_slider75c15803e4bc421ab6d6396a5ebe956b\" type=\"range\" class=\"anim-slider\"\n",
        "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
-       "           oninput=\"anime1d73e0327fa420190c43c3033a2c763.set_frame(parseInt(this.value));\">\n",
+       "           oninput=\"anim75c15803e4bc421ab6d6396a5ebe956b.set_frame(parseInt(this.value));\">\n",
        "    <div class=\"anim-buttons\">\n",
-       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anime1d73e0327fa420190c43c3033a2c763.slower()\">\n",
+       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anim75c15803e4bc421ab6d6396a5ebe956b.slower()\">\n",
        "          <i class=\"fa fa-minus\"></i></button>\n",
-       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anime1d73e0327fa420190c43c3033a2c763.first_frame()\">\n",
+       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anim75c15803e4bc421ab6d6396a5ebe956b.first_frame()\">\n",
        "        <i class=\"fa fa-fast-backward\"></i></button>\n",
-       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anime1d73e0327fa420190c43c3033a2c763.previous_frame()\">\n",
+       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anim75c15803e4bc421ab6d6396a5ebe956b.previous_frame()\">\n",
        "          <i class=\"fa fa-step-backward\"></i></button>\n",
-       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anime1d73e0327fa420190c43c3033a2c763.reverse_animation()\">\n",
+       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anim75c15803e4bc421ab6d6396a5ebe956b.reverse_animation()\">\n",
        "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
-       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anime1d73e0327fa420190c43c3033a2c763.pause_animation()\">\n",
+       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anim75c15803e4bc421ab6d6396a5ebe956b.pause_animation()\">\n",
        "          <i class=\"fa fa-pause\"></i></button>\n",
-       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anime1d73e0327fa420190c43c3033a2c763.play_animation()\">\n",
+       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anim75c15803e4bc421ab6d6396a5ebe956b.play_animation()\">\n",
        "          <i class=\"fa fa-play\"></i></button>\n",
-       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anime1d73e0327fa420190c43c3033a2c763.next_frame()\">\n",
+       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anim75c15803e4bc421ab6d6396a5ebe956b.next_frame()\">\n",
        "          <i class=\"fa fa-step-forward\"></i></button>\n",
-       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anime1d73e0327fa420190c43c3033a2c763.last_frame()\">\n",
+       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anim75c15803e4bc421ab6d6396a5ebe956b.last_frame()\">\n",
        "          <i class=\"fa fa-fast-forward\"></i></button>\n",
-       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anime1d73e0327fa420190c43c3033a2c763.faster()\">\n",
+       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anim75c15803e4bc421ab6d6396a5ebe956b.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_selecte1d73e0327fa420190c43c3033a2c763\"\n",
+       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select75c15803e4bc421ab6d6396a5ebe956b\"\n",
        "          class=\"anim-state\">\n",
-       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_e1d73e0327fa420190c43c3033a2c763\"\n",
+       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_75c15803e4bc421ab6d6396a5ebe956b\"\n",
        "             >\n",
-       "      <label for=\"_anim_radio1_e1d73e0327fa420190c43c3033a2c763\">Once</label>\n",
-       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_e1d73e0327fa420190c43c3033a2c763\"\n",
+       "      <label for=\"_anim_radio1_75c15803e4bc421ab6d6396a5ebe956b\">Once</label>\n",
+       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_75c15803e4bc421ab6d6396a5ebe956b\"\n",
        "             checked>\n",
-       "      <label for=\"_anim_radio2_e1d73e0327fa420190c43c3033a2c763\">Loop</label>\n",
-       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_e1d73e0327fa420190c43c3033a2c763\"\n",
+       "      <label for=\"_anim_radio2_75c15803e4bc421ab6d6396a5ebe956b\">Loop</label>\n",
+       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_75c15803e4bc421ab6d6396a5ebe956b\"\n",
        "             >\n",
-       "      <label for=\"_anim_radio3_e1d73e0327fa420190c43c3033a2c763\">Reflect</label>\n",
+       "      <label for=\"_anim_radio3_75c15803e4bc421ab6d6396a5ebe956b\">Reflect</label>\n",
        "    </form>\n",
        "  </div>\n",
        "</div>\n",
@@ -5941,9 +5941,9 @@
        "  /* Instantiate the Animation class. */\n",
        "  /* The IDs given should match those used in the template above. */\n",
        "  (function() {\n",
-       "    var img_id = \"_anim_imge1d73e0327fa420190c43c3033a2c763\";\n",
-       "    var slider_id = \"_anim_slidere1d73e0327fa420190c43c3033a2c763\";\n",
-       "    var loop_select_id = \"_anim_loop_selecte1d73e0327fa420190c43c3033a2c763\";\n",
+       "    var img_id = \"_anim_img75c15803e4bc421ab6d6396a5ebe956b\";\n",
+       "    var slider_id = \"_anim_slider75c15803e4bc421ab6d6396a5ebe956b\";\n",
+       "    var loop_select_id = \"_anim_loop_select75c15803e4bc421ab6d6396a5ebe956b\";\n",
        "    var frames = new Array(1);\n",
        "    \n",
        "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA8AAAALQCAYAAABfdxm0AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
@@ -6621,14 +6621,14 @@
        "    /* set a timeout to make sure all the above elements are created before\n",
        "       the object is initialized. */\n",
        "    setTimeout(function() {\n",
-       "        anime1d73e0327fa420190c43c3033a2c763 = new Animation(frames, img_id, slider_id, 200.0,\n",
+       "        anim75c15803e4bc421ab6d6396a5ebe956b = 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 0x1398bed20>"
+       "<matplotlib.animation.FuncAnimation at 0x169459b20>"
       ]
      },
      "execution_count": 147,
@@ -6660,7 +6660,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 14.2:  1.8947 seconds, answer 6876              ok"
+       "Puzzle 14.2:  1.893 seconds, answer 6876              ok"
       ]
      },
      "execution_count": 149,
@@ -6779,7 +6779,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 15.1:   .0252 seconds, answer 1563092           ok"
+       "Puzzle 15.1:   .025 seconds, answer 1563092           ok"
       ]
      },
      "execution_count": 154,
@@ -6856,7 +6856,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 15.1:   .0300 seconds, answer 1563092           ok"
+       "Puzzle 15.1:   .029 seconds, answer 1563092           ok"
       ]
      },
      "execution_count": 157,
@@ -6878,7 +6878,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 15.2:   .0427 seconds, answer 1582688           ok"
+       "Puzzle 15.2:   .042 seconds, answer 1582688           ok"
       ]
      },
      "execution_count": 158,
@@ -7035,7 +7035,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 16.1:   .1493 seconds, answer 103512            ok"
+       "Puzzle 16.1:   .147 seconds, answer 103512            ok"
       ]
      },
      "execution_count": 166,
@@ -7099,7 +7099,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 16.2:   .8634 seconds, answer 554               ok"
+       "Puzzle 16.2:   .855 seconds, answer 554               ok"
       ]
      },
      "execution_count": 169,
@@ -7231,7 +7231,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 17.1:   .0000 seconds, answer 2,1,0,1,7,2,5,0,3 ok"
+       "Puzzle 17.1:   .000 seconds, answer 2,1,0,1,7,2,5,0,3 ok"
       ]
      },
      "execution_count": 175,
@@ -7395,7 +7395,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 17.2:   .0235 seconds, answer 267265166222235   ok"
+       "Puzzle 17.2:   .024 seconds, answer 267265166222235   ok"
       ]
      },
      "execution_count": 183,
@@ -7504,7 +7504,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 18.1:   .0143 seconds, answer 344               ok"
+       "Puzzle 18.1:   .014 seconds, answer 344               ok"
       ]
      },
      "execution_count": 188,
@@ -7557,7 +7557,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 18.2:   .0323 seconds, answer 46,18             ok"
+       "Puzzle 18.2:   .033 seconds, answer 46,18             ok"
       ]
      },
      "execution_count": 191,
@@ -7657,7 +7657,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 19.1:   .0407 seconds, answer 242               ok"
+       "Puzzle 19.1:   .040 seconds, answer 242               ok"
       ]
      },
      "execution_count": 197,
@@ -7704,7 +7704,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 19.2:   .1904 seconds, answer 595975512785325   ok"
+       "Puzzle 19.2:   .183 seconds, answer 595975512785325   ok"
       ]
      },
      "execution_count": 200,
@@ -7753,7 +7753,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 19.1:   .0037 seconds, answer 242               ok"
+       "Puzzle 19.1:   .004 seconds, answer 242               ok"
       ]
      },
      "execution_count": 204,
@@ -7773,17 +7773,201 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3317844-2b4a-4756-8a59-b765aa467445",
+   "id": "efc9dc54-cdcc-40d5-85d5-b8ed8da61ba2",
    "metadata": {},
    "source": [
-    "# Summary\n",
+    "# [Day 20](https://adventofcode.com/2024/day/20): Race Condition\n",
     "\n",
-    "So far, I've solved all the puzzles. The median run time is around 10 milliseconds, but three problems take over a second."
+    "Yet another problem with a grid, this one depicting a racetrack:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 206,
+   "id": "156dcbf7-79ec-41a7-a9f2-397a827b9856",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "────────────────────────────────────────────────────────────────────────────────────────────────────\n",
+      "Puzzle input ➜ 141 strs:\n",
+      "────────────────────────────────────────────────────────────────────────────────────────────────────\n",
+      "################################################################################################ ...\n",
+      "#...#...#...........#...#...#...#...#.....#...###...#...###.........#...#...#.......#...#...#... ...\n",
+      "#.#.#.#.#.#########.#.#.#.#.#.#.#.#.#.###.#.#.###.#.#.#.###.#######.#.#.#.#.#.#####.#.#.#.#.#.#. ...\n",
+      "#.#...#.#...#.....#...#...#...#.#.#.#...#...#...#.#...#...#.......#...#...#.#.....#.#.#...#.#.#. ...\n",
+      "#.#####.###.#.###.#############.#.#.###.#######.#.#######.#######.#########.#####.#.#.#####.#.#. ...\n",
+      "#.#.....###...###.......#.......#.#.....#.......#.......#...#.....#...#.....#...#.#.#.....#...#. ...\n",
+      "#.#.###################.#.#######.#######.#############.###.#.#####.#.#.#####.#.#.#.#####.#####. ...\n",
+      "#.#.#...###...#...#.....#.......#.......#.###...#...###...#.#...#...#...###...#.#.#...###.....#. ...\n",
+      "...\n"
+     ]
+    }
+   ],
+   "source": [
+    "racetrack = Grid(parse(20))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "57918fd0-bb72-4c5e-8e1f-3bcf164a1d72",
+   "metadata": {},
+   "source": [
+    "### 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",
+    "\n",
+    "This is an all-paths-to-the-goal problem, 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": 208,
+   "id": "4c4ef05c-b548-49f9-b092-847e9752e745",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def dijkstra(grid, end_char='E') -> Dict[Point, int]:\n",
+    "    \"\"\"All-paths distances from each point to the end square on the grid: {(x, y): distance}.\"\"\"\n",
+    "    end = the(grid.findall(end_char))\n",
+    "    D = {end: 0}\n",
+    "    Q = [end]\n",
+    "    while Q:\n",
+    "        p = Q.pop()\n",
+    "        for p2 in grid.neighbors(p):\n",
+    "            if grid[p2] != '#' and p2 not in D:\n",
+    "                Q.append(p2)\n",
+    "                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 and a second step back on track.\"\"\"\n",
+    "    D = dijkstra(racetrack, '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)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 209,
+   "id": "1bbd8b72-c503-4384-aaea-a5bed45a4491",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Puzzle 20.1:   .029 seconds, answer 1343              ok"
+      ]
+     },
+     "execution_count": 209,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "answer(20.1, 1343, lambda:\n",
+    "       quantify(cheats(racetrack, 100)))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "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 problem 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",
+    "### 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 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": 211,
+   "id": "d370e24c-9b82-4415-82a5-7afe2be17654",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Puzzle 20.2:   .764 seconds, answer 982891            ok"
+      ]
+     },
+     "execution_count": 211,
+     "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",
+    "    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",
+    "\n",
+    "def neighborhood(point, radius) -> List[Point]:\n",
+    "    \"\"\"All points within `radius` of `point` (using taxi distance).\"\"\"\n",
+    "    (x, y) = point\n",
+    "    return [(x + dx, y+ dy) \n",
+    "            for dx in range(-radius, radius + 1)\n",
+    "            for dy in range(-(radius - abs(dx)), radius - abs(dx) + 1)]\n",
+    "\n",
+    "answer(20.2, 982891, lambda:\n",
+    "       quantify(big_cheats(racetrack, 100, 20)))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0022ec12-5359-455f-ace8-c8615d7cd1d2",
+   "metadata": {},
+   "source": [
+    "This solution is backwards-compatible with Part 1:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 213,
+   "id": "332e9c72-db9a-4b90-a649-45f7bf955e84",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Puzzle 20.1:   .023 seconds, answer 1343              ok"
+      ]
+     },
+     "execution_count": 213,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "answer(20.1, 1343, lambda:\n",
+    "       quantify(big_cheats(racetrack, 100, 2)))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c3317844-2b4a-4756-8a59-b765aa467445",
+   "metadata": {},
+   "source": [
+    "# Summary\n",
+    "\n",
+    "So far, I've solved all the puzzles. The median run time is about 10 milliseconds, but three problems take over a second."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 215,
    "id": "34813fc9-a000-4cd8-88ae-692851b3242c",
    "metadata": {},
    "outputs": [
@@ -7791,48 +7975,50 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Puzzle  1.1:   .0002 seconds, answer 1830467           ok\n",
-      "Puzzle  1.2:   .0001 seconds, answer 26674158          ok\n",
-      "Puzzle  2.1:   .0004 seconds, answer 257               ok\n",
-      "Puzzle  2.2:   .0022 seconds, answer 328               ok\n",
-      "Puzzle  3.1:   .0006 seconds, answer 156388521         ok\n",
-      "Puzzle  3.2:   .0004 seconds, answer 75920122          ok\n",
-      "Puzzle  4.1:   .0331 seconds, answer 2401              ok\n",
-      "Puzzle  4.2:   .0273 seconds, answer 1822              ok\n",
-      "Puzzle  5.1:   .0007 seconds, answer 5762              ok\n",
-      "Puzzle  5.2:   .0008 seconds, answer 4130              ok\n",
-      "Puzzle  6.1:   .0016 seconds, answer 5329              ok\n",
-      "Puzzle  6.2:  1.9960 seconds, answer 2162              ok\n",
-      "Puzzle  7.1:   .0137 seconds, answer 1985268524462     ok\n",
-      "Puzzle  7.2:   .6577 seconds, answer 150077710195188   ok\n",
-      "Puzzle  8.1:   .0027 seconds, answer 220               ok\n",
-      "Puzzle  8.2:   .0030 seconds, answer 813               ok\n",
-      "Puzzle  9.1:   .0202 seconds, answer 6332189866718     ok\n",
-      "Puzzle  9.2:  2.7791 seconds, answer 6353648390778     ok\n",
-      "Puzzle 10.1:   .0047 seconds, answer 744               ok\n",
-      "Puzzle 10.2:   .0062 seconds, answer 1651              ok\n",
-      "Puzzle 11.1:   .0015 seconds, answer 194482            ok\n",
-      "Puzzle 11.2:   .0596 seconds, answer 232454623677743   ok\n",
-      "Puzzle 12.1:   .0501 seconds, answer 1402544           ok\n",
-      "Puzzle 12.2:   .0423 seconds, answer 862486            ok\n",
-      "Puzzle 13.1:   .0002 seconds, answer 29598             ok\n",
-      "Puzzle 13.2:   .0004 seconds, answer 93217456941970    ok\n",
-      "Puzzle 14.1:   .0001 seconds, answer 216027840         ok\n",
-      "Puzzle 14.2:  1.8947 seconds, answer 6876              ok\n",
-      "Puzzle 15.1:   .0300 seconds, answer 1563092           ok\n",
-      "Puzzle 15.2:   .0427 seconds, answer 1582688           ok\n",
-      "Puzzle 16.1:   .1493 seconds, answer 103512            ok\n",
-      "Puzzle 16.2:   .8634 seconds, answer 554               ok\n",
-      "Puzzle 17.1:   .0000 seconds, answer 2,1,0,1,7,2,5,0,3 ok\n",
-      "Puzzle 17.2:   .0235 seconds, answer 267265166222235   ok\n",
-      "Puzzle 18.1:   .0143 seconds, answer 344               ok\n",
-      "Puzzle 18.2:   .0323 seconds, answer 46,18             ok\n",
-      "Puzzle 19.1:   .0037 seconds, answer 242               ok\n",
-      "Puzzle 19.2:   .1904 seconds, answer 595975512785325   ok\n",
+      "Puzzle  1.1:   .000 seconds, answer 1830467           ok\n",
+      "Puzzle  1.2:   .000 seconds, answer 26674158          ok\n",
+      "Puzzle  2.1:   .000 seconds, answer 257               ok\n",
+      "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:   .033 seconds, answer 2401              ok\n",
+      "Puzzle  4.2:   .027 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:  1.968 seconds, answer 2162              ok\n",
+      "Puzzle  7.1:   .014 seconds, answer 1985268524462     ok\n",
+      "Puzzle  7.2:   .656 seconds, answer 150077710195188   ok\n",
+      "Puzzle  8.1:   .003 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:  2.731 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:   .060 seconds, answer 232454623677743   ok\n",
+      "Puzzle 12.1:   .051 seconds, answer 1402544           ok\n",
+      "Puzzle 12.2:   .042 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:  1.893 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:   .147 seconds, answer 103512            ok\n",
+      "Puzzle 16.2:   .855 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:   .024 seconds, answer 267265166222235   ok\n",
+      "Puzzle 18.1:   .014 seconds, answer 344               ok\n",
+      "Puzzle 18.2:   .033 seconds, answer 46,18             ok\n",
+      "Puzzle 19.1:   .004 seconds, answer 242               ok\n",
+      "Puzzle 19.2:   .183 seconds, answer 595975512785325   ok\n",
+      "Puzzle 20.1:   .023 seconds, answer 1343              ok\n",
+      "Puzzle 20.2:   .764 seconds, answer 982891            ok\n",
       "\n",
-      "Correct: 38/38\n",
+      "Correct: 40/40\n",
       "\n",
-      "Time in seconds: 0.0099 median, 0.2355 mean, 8.9491 total.\n"
+      "Time in seconds: 0.014 median, 0.241 mean, 9.638 total.\n"
      ]
     }
    ],
diff --git a/ipynb/AdventUtils.ipynb b/ipynb/AdventUtils.ipynb
index 6a18489..fa258fd 100644
--- a/ipynb/AdventUtils.ipynb
+++ b/ipynb/AdventUtils.ipynb
@@ -194,7 +194,7 @@
     "    \n",
     "    def __repr__(self) -> str:\n",
     "        \"\"\"The repr of an answer shows what happened.\"\"\"\n",
-    "        secs    = f'{self.secs:7.4f}'.replace(' 0.', '  .')\n",
+    "        secs    = f'{self.secs:6.3f}'.replace(' 0.', '  .')\n",
     "        comment = (f'' if self.got == unknown else\n",
     "                   f' ok' if self.ok else \n",
     "                   f' WRONG; expected answer is {self.solution}')\n",
@@ -206,7 +206,7 @@
     "        print(answers[d])\n",
     "    times = [answers[d].secs for d in answers]\n",
     "    print(f'\\nCorrect: {quantify(answers[d].ok for d in answers)}/{len(answers)}')\n",
-    "    print(f'\\nTime in seconds: {median(times):.4f} median, {mean(times):.4f} mean, {sum(times):.4f} total.')"
+    "    print(f'\\nTime in seconds: {median(times):.3f} median, {mean(times):.3f} mean, {sum(times):.3f} total.')"
    ]
   },
   {