Delete Generalization_Prior_Commitment.ipynb

4fab8bc7 · Weng · eee5fa04 · eee5fa04
Commit 4fab8bc7 authored Sep 10, 2026 by Weng
--- a/Generalization_Prior_Commitment.ipynb
+++ b/Generalization_Prior_Commitment.ipynb
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "id": "40004058",
-   "metadata": {},
-   "source": [
-    "# Generalization of Prior Commitment by Simon Aronson"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "3f0faf1f",
-   "metadata": {},
-   "source": [
-    "This notebook investigates the mathematical conditions for a practically feasible version of a card trick involving two Jokers. The possible positions $a$ and $b$ of the Jokers in a deck of $N$ cards are analyzed.\n",
-    "\n",
-    "The first spectator is asked to cut off approximately a fraction $\\alpha$ of the deck, allowing for a relative deviation $\\varepsilon$. The second spectator then cuts off approximately half of the remaining cards. For different values of $\\alpha$, the notebook determines which Joker positions $(a,b)$ ensure that both cuts occur in the required regions of the deck.\n",
-    "\n",
-    "The notebook computes the set of all admissible pairs $(a,b)$ and to identify suitable configurations for performing the trick in practice."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "70488098",
-   "metadata": {},
-   "source": [
-    "## Version with $\\alpha \\in [0.25,0.5]$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "id": "2c46c5fb",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import numpy as np\n",
-    "from math import ceil, floor\n",
-    "\n",
-    "N=54 #size of the deck\n",
-    "epsilon=0.2 #deviation\n",
-    "\n",
-    "possible_solutions=set()\n",
-    "alphas = np.linspace(1/4, 1/2, 100).tolist()\n",
-    "for alpha in alphas:\n",
-    "    s=ceil(alpha*N*(1-epsilon))\n",
-    "    for a in range(1,s):\n",
-    "        t=floor(alpha*N*(1+epsilon))+1\n",
-    "        for b in range(t+1,N):\n",
-    "            if (b<(N-s)/2*(1-epsilon)+s):\n",
-    "                possible_solutions.add((a,b))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "id": "c8192676",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "272"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(possible_solutions)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "25e91ad8",
-   "metadata": {},
-   "source": [
-    "## Discrete version with $\\alpha\\in\\{0.25,0.33,0.5\\}$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "id": "e2fecd60",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "N=54 #size of the deck\n",
-    "epsilon=0.2 #deviation\n",
-    "\n",
-    "possible_solutions=set()\n",
-    "alphas = [0.25,0.33,0.5]\n",
-    "for alpha in alphas:\n",
-    "    s=ceil(alpha*N*(1-epsilon))\n",
-    "    for a in range(1,s):\n",
-    "        t=floor(alpha*N*(1+epsilon))+1\n",
-    "        for b in range(t+1,N):\n",
-    "            if (b<(N-s)/2*(1-epsilon)+s):\n",
-    "                possible_solutions.add((a,b))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "id": "7a425763",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "183"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(possible_solutions)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "id": "c2cd69c9",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "(1, 18, 16, 52, 0.25)\n",
-      "(1, 19, 17, 52, 0.25)\n",
-      "(1, 20, 18, 52, 0.25)\n",
-      "(1, 21, 19, 52, 0.25)\n",
-      "(1, 22, 20, 52, 0.25)\n",
-      "(1, 23, 21, 52, 0.25)\n",
-      "(1, 24, 22, 52, 0.25)\n",
-      "(1, 25, 23, 52, 0.25)\n",
-      "(1, 26, 24, 52, 0.25)\n",
-      "(1, 27, 25, 52, 0.25)\n",
-      "(1, 28, 26, 52, 0.25)\n",
-      "(2, 18, 15, 51, 0.25)\n",
-      "(2, 19, 16, 51, 0.25)\n",
-      "(2, 20, 17, 51, 0.25)\n",
-      "(2, 21, 18, 51, 0.25)\n",
-      "(2, 22, 19, 51, 0.25)\n",
-      "(2, 23, 20, 51, 0.25)\n",
-      "(2, 24, 21, 51, 0.25)\n",
-      "(2, 25, 22, 51, 0.25)\n",
-      "(2, 26, 23, 51, 0.25)\n",
-      "(2, 27, 24, 51, 0.25)\n",
-      "(2, 28, 25, 51, 0.25)\n",
-      "(3, 18, 14, 50, 0.25)\n",
-      "(3, 19, 15, 50, 0.25)\n",
-      "(3, 20, 16, 50, 0.25)\n",
-      "(3, 21, 17, 50, 0.25)\n",
-      "(3, 22, 18, 50, 0.25)\n",
-      "(3, 23, 19, 50, 0.25)\n",
-      "(3, 24, 20, 50, 0.25)\n",
-      "(3, 25, 21, 50, 0.25)\n",
-      "(3, 26, 22, 50, 0.25)\n",
-      "(3, 27, 23, 50, 0.25)\n",
-      "(3, 28, 24, 50, 0.25)\n",
-      "(4, 18, 13, 49, 0.25)\n",
-      "(4, 19, 14, 49, 0.25)\n",
-      "(4, 20, 15, 49, 0.25)\n",
-      "(4, 21, 16, 49, 0.25)\n",
-      "(4, 22, 17, 49, 0.25)\n",
-      "(4, 23, 18, 49, 0.25)\n",
-      "(4, 24, 19, 49, 0.25)\n",
-      "(4, 25, 20, 49, 0.25)\n",
-      "(4, 26, 21, 49, 0.25)\n",
-      "(4, 27, 22, 49, 0.25)\n",
-      "(4, 28, 23, 49, 0.25)\n",
-      "(5, 18, 12, 48, 0.25)\n",
-      "(5, 19, 13, 48, 0.25)\n",
-      "(5, 20, 14, 48, 0.25)\n",
-      "(5, 21, 15, 48, 0.25)\n",
-      "(5, 22, 16, 48, 0.25)\n",
-      "(5, 23, 17, 48, 0.25)\n",
-      "(5, 24, 18, 48, 0.25)\n",
-      "(5, 25, 19, 48, 0.25)\n",
-      "(5, 26, 20, 48, 0.25)\n",
-      "(5, 27, 21, 48, 0.25)\n",
-      "(5, 28, 22, 48, 0.25)\n",
-      "(6, 18, 11, 47, 0.25)\n",
-      "(6, 19, 12, 47, 0.25)\n",
-      "(6, 20, 13, 47, 0.25)\n",
-      "(6, 21, 14, 47, 0.25)\n",
-      "(6, 22, 15, 47, 0.25)\n",
-      "(6, 23, 16, 47, 0.25)\n",
-      "(6, 24, 17, 47, 0.25)\n",
-      "(6, 25, 18, 47, 0.25)\n",
-      "(6, 26, 19, 47, 0.25)\n",
-      "(6, 27, 20, 47, 0.25)\n",
-      "(6, 28, 21, 47, 0.25)\n",
-      "(7, 18, 10, 46, 0.25)\n",
-      "(7, 19, 11, 46, 0.25)\n",
-      "(7, 20, 12, 46, 0.25)\n",
-      "(7, 21, 13, 46, 0.25)\n",
-      "(7, 22, 14, 46, 0.25)\n",
-      "(7, 23, 15, 46, 0.25)\n",
-      "(7, 24, 16, 46, 0.25)\n",
-      "(7, 25, 17, 46, 0.25)\n",
-      "(7, 26, 18, 46, 0.25)\n",
-      "(7, 27, 19, 46, 0.25)\n",
-      "(7, 28, 20, 46, 0.25)\n",
-      "(8, 18, 9, 45, 0.25)\n",
-      "(8, 19, 10, 45, 0.25)\n",
-      "(8, 20, 11, 45, 0.25)\n",
-      "(8, 21, 12, 45, 0.25)\n",
-      "(8, 22, 13, 45, 0.25)\n",
-      "(8, 23, 14, 45, 0.25)\n",
-      "(8, 24, 15, 45, 0.25)\n",
-      "(8, 25, 16, 45, 0.25)\n",
-      "(8, 26, 17, 45, 0.25)\n",
-      "(8, 27, 18, 45, 0.25)\n",
-      "(8, 28, 19, 45, 0.25)\n",
-      "(9, 18, 8, 44, 0.25)\n",
-      "(9, 19, 9, 44, 0.25)\n",
-      "(9, 20, 10, 44, 0.25)\n",
-      "(9, 21, 11, 44, 0.25)\n",
-      "(9, 22, 12, 44, 0.25)\n",
-      "(9, 23, 13, 44, 0.25)\n",
-      "(9, 24, 14, 44, 0.25)\n",
-      "(9, 25, 15, 44, 0.25)\n",
-      "(9, 26, 16, 44, 0.25)\n",
-      "(9, 27, 17, 44, 0.25)\n",
-      "(9, 28, 18, 44, 0.25)\n",
-      "(10, 18, 7, 43, 0.25)\n",
-      "(10, 19, 8, 43, 0.25)\n",
-      "(10, 20, 9, 43, 0.25)\n",
-      "(10, 21, 10, 43, 0.25)\n",
-      "(10, 22, 11, 43, 0.25)\n",
-      "(10, 23, 12, 43, 0.25)\n",
-      "(10, 24, 13, 43, 0.25)\n",
-      "(10, 25, 14, 43, 0.25)\n",
-      "(10, 26, 15, 43, 0.25)\n",
-      "(10, 27, 16, 43, 0.25)\n",
-      "(10, 28, 17, 43, 0.25)\n",
-      "(1, 23, 21, 52, 0.33)\n",
-      "(1, 24, 22, 52, 0.33)\n",
-      "(1, 25, 23, 52, 0.33)\n",
-      "(1, 26, 24, 52, 0.33)\n",
-      "(1, 27, 25, 52, 0.33)\n",
-      "(1, 28, 26, 52, 0.33)\n",
-      "(1, 29, 27, 52, 0.33)\n",
-      "(1, 30, 28, 52, 0.33)\n",
-      "(2, 23, 20, 51, 0.33)\n",
-      "(2, 24, 21, 51, 0.33)\n",
-      "(2, 25, 22, 51, 0.33)\n",
-      "(2, 26, 23, 51, 0.33)\n",
-      "(2, 27, 24, 51, 0.33)\n",
-      "(2, 28, 25, 51, 0.33)\n",
-      "(2, 29, 26, 51, 0.33)\n",
-      "(2, 30, 27, 51, 0.33)\n",
-      "(3, 23, 19, 50, 0.33)\n",
-      "(3, 24, 20, 50, 0.33)\n",
-      "(3, 25, 21, 50, 0.33)\n",
-      "(3, 26, 22, 50, 0.33)\n",
-      "(3, 27, 23, 50, 0.33)\n",
-      "(3, 28, 24, 50, 0.33)\n",
-      "(3, 29, 25, 50, 0.33)\n",
-      "(3, 30, 26, 50, 0.33)\n",
-      "(4, 23, 18, 49, 0.33)\n",
-      "(4, 24, 19, 49, 0.33)\n",
-      "(4, 25, 20, 49, 0.33)\n",
-      "(4, 26, 21, 49, 0.33)\n",
-      "(4, 27, 22, 49, 0.33)\n",
-      "(4, 28, 23, 49, 0.33)\n",
-      "(4, 29, 24, 49, 0.33)\n",
-      "(4, 30, 25, 49, 0.33)\n",
-      "(5, 23, 17, 48, 0.33)\n",
-      "(5, 24, 18, 48, 0.33)\n",
-      "(5, 25, 19, 48, 0.33)\n",
-      "(5, 26, 20, 48, 0.33)\n",
-      "(5, 27, 21, 48, 0.33)\n",
-      "(5, 28, 22, 48, 0.33)\n",
-      "(5, 29, 23, 48, 0.33)\n",
-      "(5, 30, 24, 48, 0.33)\n",
-      "(6, 23, 16, 47, 0.33)\n",
-      "(6, 24, 17, 47, 0.33)\n",
-      "(6, 25, 18, 47, 0.33)\n",
-      "(6, 26, 19, 47, 0.33)\n",
-      "(6, 27, 20, 47, 0.33)\n",
-      "(6, 28, 21, 47, 0.33)\n",
-      "(6, 29, 22, 47, 0.33)\n",
-      "(6, 30, 23, 47, 0.33)\n",
-      "(7, 23, 15, 46, 0.33)\n",
-      "(7, 24, 16, 46, 0.33)\n",
-      "(7, 25, 17, 46, 0.33)\n",
-      "(7, 26, 18, 46, 0.33)\n",
-      "(7, 27, 19, 46, 0.33)\n",
-      "(7, 28, 20, 46, 0.33)\n",
-      "(7, 29, 21, 46, 0.33)\n",
-      "(7, 30, 22, 46, 0.33)\n",
-      "(8, 23, 14, 45, 0.33)\n",
-      "(8, 24, 15, 45, 0.33)\n",
-      "(8, 25, 16, 45, 0.33)\n",
-      "(8, 26, 17, 45, 0.33)\n",
-      "(8, 27, 18, 45, 0.33)\n",
-      "(8, 28, 19, 45, 0.33)\n",
-      "(8, 29, 20, 45, 0.33)\n",
-      "(8, 30, 21, 45, 0.33)\n",
-      "(9, 23, 13, 44, 0.33)\n",
-      "(9, 24, 14, 44, 0.33)\n",
-      "(9, 25, 15, 44, 0.33)\n",
-      "(9, 26, 16, 44, 0.33)\n",
-      "(9, 27, 17, 44, 0.33)\n",
-      "(9, 28, 18, 44, 0.33)\n",
-      "(9, 29, 19, 44, 0.33)\n",
-      "(9, 30, 20, 44, 0.33)\n",
-      "(10, 23, 12, 43, 0.33)\n",
-      "(10, 24, 13, 43, 0.33)\n",
-      "(10, 25, 14, 43, 0.33)\n",
-      "(10, 26, 15, 43, 0.33)\n",
-      "(10, 27, 16, 43, 0.33)\n",
-      "(10, 28, 17, 43, 0.33)\n",
-      "(10, 29, 18, 43, 0.33)\n",
-      "(10, 30, 19, 43, 0.33)\n",
-      "(11, 23, 11, 42, 0.33)\n",
-      "(11, 24, 12, 42, 0.33)\n",
-      "(11, 25, 13, 42, 0.33)\n",
-      "(11, 26, 14, 42, 0.33)\n",
-      "(11, 27, 15, 42, 0.33)\n",
-      "(11, 28, 16, 42, 0.33)\n",
-      "(11, 29, 17, 42, 0.33)\n",
-      "(11, 30, 18, 42, 0.33)\n",
-      "(12, 23, 10, 41, 0.33)\n",
-      "(12, 24, 11, 41, 0.33)\n",
-      "(12, 25, 12, 41, 0.33)\n",
-      "(12, 26, 13, 41, 0.33)\n",
-      "(12, 27, 14, 41, 0.33)\n",
-      "(12, 28, 15, 41, 0.33)\n",
-      "(12, 29, 16, 41, 0.33)\n",
-      "(12, 30, 17, 41, 0.33)\n",
-      "(13, 23, 9, 40, 0.33)\n",
-      "(13, 24, 10, 40, 0.33)\n",
-      "(13, 25, 11, 40, 0.33)\n",
-      "(13, 26, 12, 40, 0.33)\n",
-      "(13, 27, 13, 40, 0.33)\n",
-      "(13, 28, 14, 40, 0.33)\n",
-      "(13, 29, 15, 40, 0.33)\n",
-      "(13, 30, 16, 40, 0.33)\n",
-      "(14, 23, 8, 39, 0.33)\n",
-      "(14, 24, 9, 39, 0.33)\n",
-      "(14, 25, 10, 39, 0.33)\n",
-      "(14, 26, 11, 39, 0.33)\n",
-      "(14, 27, 12, 39, 0.33)\n",
-      "(14, 28, 13, 39, 0.33)\n",
-      "(14, 29, 14, 39, 0.33)\n",
-      "(14, 30, 15, 39, 0.33)\n",
-      "(1, 34, 32, 52, 0.5)\n",
-      "(2, 34, 31, 51, 0.5)\n",
-      "(3, 34, 30, 50, 0.5)\n",
-      "(4, 34, 29, 49, 0.5)\n",
-      "(5, 34, 28, 48, 0.5)\n",
-      "(6, 34, 27, 47, 0.5)\n",
-      "(7, 34, 26, 46, 0.5)\n",
-      "(8, 34, 25, 45, 0.5)\n",
-      "(9, 34, 24, 44, 0.5)\n",
-      "(10, 34, 23, 43, 0.5)\n",
-      "(11, 34, 22, 42, 0.5)\n",
-      "(12, 34, 21, 41, 0.5)\n",
-      "(13, 34, 20, 40, 0.5)\n",
-      "(14, 34, 19, 39, 0.5)\n",
-      "(15, 34, 18, 38, 0.5)\n",
-      "(16, 34, 17, 37, 0.5)\n",
-      "(17, 34, 16, 36, 0.5)\n",
-      "(18, 34, 15, 35, 0.5)\n",
-      "(19, 34, 14, 34, 0.5)\n",
-      "(20, 34, 13, 33, 0.5)\n",
-      "(21, 34, 12, 32, 0.5)\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "243"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "N=54 #size of the deck\n",
-    "epsilon=0.2 #deviation\n",
-    "\n",
-    "possible_solutions=set()\n",
-    "alphas = [0.25,0.33,0.5]\n",
-    "for alpha in alphas:\n",
-    "    s=ceil(alpha*N*(1-epsilon))\n",
-    "    for a in range(1,s):\n",
-    "        t=floor(alpha*N*(1+epsilon))+1\n",
-    "        for b in range(t+1,N):\n",
-    "            if (b<(N-s)/2*(1-epsilon)+s):\n",
-    "                print((a,b,b-a-1,N-a-1,alpha))\n",
-    "                possible_solutions.add((a,b,b-a-1,N-a-1,alpha))\n",
-    "len(possible_solutions)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "5a1398fa",
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.10.12"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
-%% Cell type:markdown id:40004058 tags:
-
-# Generalization of Prior Commitment by Simon Aronson
-
-%% Cell type:markdown id:3f0faf1f tags:
-
-This notebook investigates the mathematical conditions for a practically feasible version of a card trick involving two Jokers. The possible positions $a$ and $b$ of the Jokers in a deck of $N$ cards are analyzed.
-
-The first spectator is asked to cut off approximately a fraction $\alpha$ of the deck, allowing for a relative deviation $\varepsilon$. The second spectator then cuts off approximately half of the remaining cards. For different values of $\alpha$, the notebook determines which Joker positions $(a,b)$ ensure that both cuts occur in the required regions of the deck.
-
-The notebook computes the set of all admissible pairs $(a,b)$ and to identify suitable configurations for performing the trick in practice.
-
-%% Cell type:markdown id:70488098 tags:
-
-## Version with $\alpha \in [0.25,0.5]$
-
-%% Cell type:code id:2c46c5fb tags:
-
-``` python
-import numpy as np
-from math import ceil, floor
-
-N=54 #size of the deck
-epsilon=0.2 #deviation
-
-possible_solutions=set()
-alphas = np.linspace(1/4, 1/2, 100).tolist()
-for alpha in alphas:
-    s=ceil(alpha*N*(1-epsilon))
-    for a in range(1,s):
-        t=floor(alpha*N*(1+epsilon))+1
-        for b in range(t+1,N):
-            if (b<(N-s)/2*(1-epsilon)+s):
-                possible_solutions.add((a,b))
-```
-
-%% Cell type:code id:c8192676 tags:
-
-``` python
-len(possible_solutions)
-```
-
-%% Output
-
-    272
-
-%% Cell type:markdown id:25e91ad8 tags:
-
-## Discrete version with $\alpha\in\{0.25,0.33,0.5\}$
-
-%% Cell type:code id:e2fecd60 tags:
-
-``` python
-N=54 #size of the deck
-epsilon=0.2 #deviation
-
-possible_solutions=set()
-alphas = [0.25,0.33,0.5]
-for alpha in alphas:
-    s=ceil(alpha*N*(1-epsilon))
-    for a in range(1,s):
-        t=floor(alpha*N*(1+epsilon))+1
-        for b in range(t+1,N):
-            if (b<(N-s)/2*(1-epsilon)+s):
-                possible_solutions.add((a,b))
-```
-
-%% Cell type:code id:7a425763 tags:
-
-``` python
-len(possible_solutions)
-```
-
-%% Output
-
-    183
-
-%% Cell type:code id:c2cd69c9 tags:
-
-``` python
-N=54 #size of the deck
-epsilon=0.2 #deviation
-
-possible_solutions=set()
-alphas = [0.25,0.33,0.5]
-for alpha in alphas:
-    s=ceil(alpha*N*(1-epsilon))
-    for a in range(1,s):
-        t=floor(alpha*N*(1+epsilon))+1
-        for b in range(t+1,N):
-            if (b<(N-s)/2*(1-epsilon)+s):
-                print((a,b,b-a-1,N-a-1,alpha))
-                possible_solutions.add((a,b,b-a-1,N-a-1,alpha))
-len(possible_solutions)
-```
-
-%% Output
-
-    (1, 18, 16, 52, 0.25)
-    (1, 19, 17, 52, 0.25)
-    (1, 20, 18, 52, 0.25)
-    (1, 21, 19, 52, 0.25)
-    (1, 22, 20, 52, 0.25)
-    (1, 23, 21, 52, 0.25)
-    (1, 24, 22, 52, 0.25)
-    (1, 25, 23, 52, 0.25)
-    (1, 26, 24, 52, 0.25)
-    (1, 27, 25, 52, 0.25)
-    (1, 28, 26, 52, 0.25)
-    (2, 18, 15, 51, 0.25)
-    (2, 19, 16, 51, 0.25)
-    (2, 20, 17, 51, 0.25)
-    (2, 21, 18, 51, 0.25)
-    (2, 22, 19, 51, 0.25)
-    (2, 23, 20, 51, 0.25)
-    (2, 24, 21, 51, 0.25)
-    (2, 25, 22, 51, 0.25)
-    (2, 26, 23, 51, 0.25)
-    (2, 27, 24, 51, 0.25)
-    (2, 28, 25, 51, 0.25)
-    (3, 18, 14, 50, 0.25)
-    (3, 19, 15, 50, 0.25)
-    (3, 20, 16, 50, 0.25)
-    (3, 21, 17, 50, 0.25)
-    (3, 22, 18, 50, 0.25)
-    (3, 23, 19, 50, 0.25)
-    (3, 24, 20, 50, 0.25)
-    (3, 25, 21, 50, 0.25)
-    (3, 26, 22, 50, 0.25)
-    (3, 27, 23, 50, 0.25)
-    (3, 28, 24, 50, 0.25)
-    (4, 18, 13, 49, 0.25)
-    (4, 19, 14, 49, 0.25)
-    (4, 20, 15, 49, 0.25)
-    (4, 21, 16, 49, 0.25)
-    (4, 22, 17, 49, 0.25)
-    (4, 23, 18, 49, 0.25)
-    (4, 24, 19, 49, 0.25)
-    (4, 25, 20, 49, 0.25)
-    (4, 26, 21, 49, 0.25)
-    (4, 27, 22, 49, 0.25)
-    (4, 28, 23, 49, 0.25)
-    (5, 18, 12, 48, 0.25)
-    (5, 19, 13, 48, 0.25)
-    (5, 20, 14, 48, 0.25)
-    (5, 21, 15, 48, 0.25)
-    (5, 22, 16, 48, 0.25)
-    (5, 23, 17, 48, 0.25)
-    (5, 24, 18, 48, 0.25)
-    (5, 25, 19, 48, 0.25)
-    (5, 26, 20, 48, 0.25)
-    (5, 27, 21, 48, 0.25)
-    (5, 28, 22, 48, 0.25)
-    (6, 18, 11, 47, 0.25)
-    (6, 19, 12, 47, 0.25)
-    (6, 20, 13, 47, 0.25)
-    (6, 21, 14, 47, 0.25)
-    (6, 22, 15, 47, 0.25)
-    (6, 23, 16, 47, 0.25)
-    (6, 24, 17, 47, 0.25)
-    (6, 25, 18, 47, 0.25)
-    (6, 26, 19, 47, 0.25)
-    (6, 27, 20, 47, 0.25)
-    (6, 28, 21, 47, 0.25)
-    (7, 18, 10, 46, 0.25)
-    (7, 19, 11, 46, 0.25)
-    (7, 20, 12, 46, 0.25)
-    (7, 21, 13, 46, 0.25)
-    (7, 22, 14, 46, 0.25)
-    (7, 23, 15, 46, 0.25)
-    (7, 24, 16, 46, 0.25)
-    (7, 25, 17, 46, 0.25)
-    (7, 26, 18, 46, 0.25)
-    (7, 27, 19, 46, 0.25)
-    (7, 28, 20, 46, 0.25)
-    (8, 18, 9, 45, 0.25)
-    (8, 19, 10, 45, 0.25)
-    (8, 20, 11, 45, 0.25)
-    (8, 21, 12, 45, 0.25)
-    (8, 22, 13, 45, 0.25)
-    (8, 23, 14, 45, 0.25)
-    (8, 24, 15, 45, 0.25)
-    (8, 25, 16, 45, 0.25)
-    (8, 26, 17, 45, 0.25)
-    (8, 27, 18, 45, 0.25)
-    (8, 28, 19, 45, 0.25)
-    (9, 18, 8, 44, 0.25)
-    (9, 19, 9, 44, 0.25)
-    (9, 20, 10, 44, 0.25)
-    (9, 21, 11, 44, 0.25)
-    (9, 22, 12, 44, 0.25)
-    (9, 23, 13, 44, 0.25)
-    (9, 24, 14, 44, 0.25)
-    (9, 25, 15, 44, 0.25)
-    (9, 26, 16, 44, 0.25)
-    (9, 27, 17, 44, 0.25)
-    (9, 28, 18, 44, 0.25)
-    (10, 18, 7, 43, 0.25)
-    (10, 19, 8, 43, 0.25)
-    (10, 20, 9, 43, 0.25)
-    (10, 21, 10, 43, 0.25)
-    (10, 22, 11, 43, 0.25)
-    (10, 23, 12, 43, 0.25)
-    (10, 24, 13, 43, 0.25)
-    (10, 25, 14, 43, 0.25)
-    (10, 26, 15, 43, 0.25)
-    (10, 27, 16, 43, 0.25)
-    (10, 28, 17, 43, 0.25)
-    (1, 23, 21, 52, 0.33)
-    (1, 24, 22, 52, 0.33)
-    (1, 25, 23, 52, 0.33)
-    (1, 26, 24, 52, 0.33)
-    (1, 27, 25, 52, 0.33)
-    (1, 28, 26, 52, 0.33)
-    (1, 29, 27, 52, 0.33)
-    (1, 30, 28, 52, 0.33)
-    (2, 23, 20, 51, 0.33)
-    (2, 24, 21, 51, 0.33)
-    (2, 25, 22, 51, 0.33)
-    (2, 26, 23, 51, 0.33)
-    (2, 27, 24, 51, 0.33)
-    (2, 28, 25, 51, 0.33)
-    (2, 29, 26, 51, 0.33)
-    (2, 30, 27, 51, 0.33)
-    (3, 23, 19, 50, 0.33)
-    (3, 24, 20, 50, 0.33)
-    (3, 25, 21, 50, 0.33)
-    (3, 26, 22, 50, 0.33)
-    (3, 27, 23, 50, 0.33)
-    (3, 28, 24, 50, 0.33)
-    (3, 29, 25, 50, 0.33)
-    (3, 30, 26, 50, 0.33)
-    (4, 23, 18, 49, 0.33)
-    (4, 24, 19, 49, 0.33)
-    (4, 25, 20, 49, 0.33)
-    (4, 26, 21, 49, 0.33)
-    (4, 27, 22, 49, 0.33)
-    (4, 28, 23, 49, 0.33)
-    (4, 29, 24, 49, 0.33)
-    (4, 30, 25, 49, 0.33)
-    (5, 23, 17, 48, 0.33)
-    (5, 24, 18, 48, 0.33)
-    (5, 25, 19, 48, 0.33)
-    (5, 26, 20, 48, 0.33)
-    (5, 27, 21, 48, 0.33)
-    (5, 28, 22, 48, 0.33)
-    (5, 29, 23, 48, 0.33)
-    (5, 30, 24, 48, 0.33)
-    (6, 23, 16, 47, 0.33)
-    (6, 24, 17, 47, 0.33)
-    (6, 25, 18, 47, 0.33)
-    (6, 26, 19, 47, 0.33)
-    (6, 27, 20, 47, 0.33)
-    (6, 28, 21, 47, 0.33)
-    (6, 29, 22, 47, 0.33)
-    (6, 30, 23, 47, 0.33)
-    (7, 23, 15, 46, 0.33)
-    (7, 24, 16, 46, 0.33)
-    (7, 25, 17, 46, 0.33)
-    (7, 26, 18, 46, 0.33)
-    (7, 27, 19, 46, 0.33)
-    (7, 28, 20, 46, 0.33)
-    (7, 29, 21, 46, 0.33)
-    (7, 30, 22, 46, 0.33)
-    (8, 23, 14, 45, 0.33)
-    (8, 24, 15, 45, 0.33)
-    (8, 25, 16, 45, 0.33)
-    (8, 26, 17, 45, 0.33)
-    (8, 27, 18, 45, 0.33)
-    (8, 28, 19, 45, 0.33)
-    (8, 29, 20, 45, 0.33)
-    (8, 30, 21, 45, 0.33)
-    (9, 23, 13, 44, 0.33)
-    (9, 24, 14, 44, 0.33)
-    (9, 25, 15, 44, 0.33)
-    (9, 26, 16, 44, 0.33)
-    (9, 27, 17, 44, 0.33)
-    (9, 28, 18, 44, 0.33)
-    (9, 29, 19, 44, 0.33)
-    (9, 30, 20, 44, 0.33)
-    (10, 23, 12, 43, 0.33)
-    (10, 24, 13, 43, 0.33)
-    (10, 25, 14, 43, 0.33)
-    (10, 26, 15, 43, 0.33)
-    (10, 27, 16, 43, 0.33)
-    (10, 28, 17, 43, 0.33)
-    (10, 29, 18, 43, 0.33)
-    (10, 30, 19, 43, 0.33)
-    (11, 23, 11, 42, 0.33)
-    (11, 24, 12, 42, 0.33)
-    (11, 25, 13, 42, 0.33)
-    (11, 26, 14, 42, 0.33)
-    (11, 27, 15, 42, 0.33)
-    (11, 28, 16, 42, 0.33)
-    (11, 29, 17, 42, 0.33)
-    (11, 30, 18, 42, 0.33)
-    (12, 23, 10, 41, 0.33)
-    (12, 24, 11, 41, 0.33)
-    (12, 25, 12, 41, 0.33)
-    (12, 26, 13, 41, 0.33)
-    (12, 27, 14, 41, 0.33)
-    (12, 28, 15, 41, 0.33)
-    (12, 29, 16, 41, 0.33)
-    (12, 30, 17, 41, 0.33)
-    (13, 23, 9, 40, 0.33)
-    (13, 24, 10, 40, 0.33)
-    (13, 25, 11, 40, 0.33)
-    (13, 26, 12, 40, 0.33)
-    (13, 27, 13, 40, 0.33)
-    (13, 28, 14, 40, 0.33)
-    (13, 29, 15, 40, 0.33)
-    (13, 30, 16, 40, 0.33)
-    (14, 23, 8, 39, 0.33)
-    (14, 24, 9, 39, 0.33)
-    (14, 25, 10, 39, 0.33)
-    (14, 26, 11, 39, 0.33)
-    (14, 27, 12, 39, 0.33)
-    (14, 28, 13, 39, 0.33)
-    (14, 29, 14, 39, 0.33)
-    (14, 30, 15, 39, 0.33)
-    (1, 34, 32, 52, 0.5)
-    (2, 34, 31, 51, 0.5)
-    (3, 34, 30, 50, 0.5)
-    (4, 34, 29, 49, 0.5)
-    (5, 34, 28, 48, 0.5)
-    (6, 34, 27, 47, 0.5)
-    (7, 34, 26, 46, 0.5)
-    (8, 34, 25, 45, 0.5)
-    (9, 34, 24, 44, 0.5)
-    (10, 34, 23, 43, 0.5)
-    (11, 34, 22, 42, 0.5)
-    (12, 34, 21, 41, 0.5)
-    (13, 34, 20, 40, 0.5)
-    (14, 34, 19, 39, 0.5)
-    (15, 34, 18, 38, 0.5)
-    (16, 34, 17, 37, 0.5)
-    (17, 34, 16, 36, 0.5)
-    (18, 34, 15, 35, 0.5)
-    (19, 34, 14, 34, 0.5)
-    (20, 34, 13, 33, 0.5)
-    (21, 34, 12, 32, 0.5)
-
-    243
-
-%% Cell type:code id:5a1398fa tags:
-
-``` python
-```