Placement puzzle picture

placement.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n",
      "4\n",
      "6\n",
      "8\n",
      "10\n",
      "12\n",
      "14\n",
      "16\n",
      "18\n",
      "20\n",
      "22\n",
      "24\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 720x960 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 30\n",
    "\n",
    "def prob_chart(N):\n",
    "    if N<=0:\n",
    "        return [[0]]\n",
    "    probs = [1]+[0]*(N)\n",
    "    allprobs = []\n",
    "    for i in range(N):\n",
    "        probs = [probs[i]*i/N + (probs[i-1]*(1-(i-1)/N) if i>0 else 0) for i in range(len(probs))]\n",
    "        allprobs.append(probs[1:])\n",
    "    return allprobs\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "\n",
    "matplotlib.rcParams['image.composite_image'] = False\n",
    "\n",
    "w,h = 3,4\n",
    "s = 10\n",
    "fig, axs = plt.subplots(h,w,figsize=(s,s*h/w))\n",
    "for y,arow in enumerate(axs):\n",
    "    for x,ax in enumerate(arow):\n",
    "        N = (w*y+x+1)*2\n",
    "        print(N)\n",
    "        ax.matshow(prob_chart(N))\n",
    "        ax.axis('off')\n",
    "#plt.show()\n",
    "plt.savefig(\"placement.svg\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 340,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "44\n"
     ]
    },
    {
     "data": {
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