{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from __future__ import division\n",
    "# we have 13 virtual mice, mouse number 0,4,8 are \"empty\" mice.\n",
    "wine_groups_for_virtual_mice = [set() for i in range(13)]\n",
    "for i in range(1000):\n",
    "    i0 = i%80\n",
    "    i1 = i0%4\n",
    "    i2 = (i0//4)%4\n",
    "    i3 = i0//16\n",
    "    wine_groups_for_virtual_mice[i1].add(i)\n",
    "    wine_groups_for_virtual_mice[4+i2].add(i)\n",
    "    wine_groups_for_virtual_mice[8+i3].add(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 2, 4, 8, 9, 10, 12, 16, 17, 18, 20, 32, 33, 34, 36, 64, 65, 66, 68, 72, 73, 74, 76, 80, 81, 82, 84, 96, 97, 98, 100, 128, 129, 130, 132, 136, 137, 138, 140, 144, 145, 146, 148, 160, 161, 162, 164, 256, 257, 258, 260, 264, 265, 266, 268, 272, 273, 274, 276, 288, 289, 290, 292, 512, 513, 514, 516, 520, 521, 522, 524, 528, 529, 530, 532, 544, 545, 546, 548, 0, 1, 2, 4, 8, 9, 10, 12, 16, 17, 18, 20, 32, 33, 34, 36, 64, 65, 66, 68, 72, 73, 74, 76, 80, 81, 82, 84, 96, 97, 98, 100, 128, 129, 130, 132, 136, 137, 138, 140, 144, 145, 146, 148, 160, 161, 162, 164, 256, 257, 258, 260, 264, 265, 266, 268, 272, 273, 274, 276, 288, 289, 290, 292, 512, 513, 514, 516, 520, 521, 522, 524, 528, 529, 530, 532, 544, 545, 546, 548, 0, 1, 2, 4, 8, 9, 10, 12, 16, 17, 18, 20, 32, 33, 34, 36, 64, 65, 66, 68, 72, 73, 74, 76, 80, 81, 82, 84, 96, 97, 98, 100, 128, 129, 130, 132, 136, 137, 138, 140, 144, 145, 146, 148, 160, 161, 162, 164, 256, 257, 258, 260, 264, 265, 266, 268, 272, 273, 274, 276, 288, 289, 290, 292, 512, 513, 514, 516, 520, 521, 522, 524, 528, 529, 530, 532, 544, 545, 546, 548, 0, 1, 2, 4, 8, 9, 10, 12, 16, 17, 18, 20, 32, 33, 34, 36, 64, 65, 66, 68, 72, 73, 74, 76, 80, 81, 82, 84, 96, 97, 98, 100, 128, 129, 130, 132, 136, 137, 138, 140, 144, 145, 146, 148, 160, 161, 162, 164, 256, 257, 258, 260, 264, 265, 266, 268, 272, 273, 274, 276, 288, 289, 290, 292, 512, 513, 514, 516, 520, 521, 522, 524, 528, 529, 530, 532, 544, 545, 546, 548, 0, 1, 2, 4, 8, 9, 10, 12, 16, 17, 18, 20, 32, 33, 34, 36, 64, 65, 66, 68, 72, 73, 74, 76, 80, 81, 82, 84, 96, 97, 98, 100, 128, 129, 130, 132, 136, 137, 138, 140, 144, 145, 146, 148, 160, 161, 162, 164, 256, 257, 258, 260, 264, 265, 266, 268, 272, 273, 274, 276, 288, 289, 290, 292, 512, 513, 514, 516, 520, 521, 522, 524, 528, 529, 530, 532, 544, 545, 546, 548, 0, 1, 2, 4, 8, 9, 10, 12, 16, 17, 18, 20, 32, 33, 34, 36, 64, 65, 66, 68, 72, 73, 74, 76, 80, 81, 82, 84, 96, 97, 98, 100, 128, 129, 130, 132, 136, 137, 138, 140, 144, 145, 146, 148, 160, 161, 162, 164, 256, 257, 258, 260, 264, 265, 266, 268, 272, 273, 274, 276, 288, 289, 290, 292, 512, 513, 514, 516, 520, 521, 522, 524, 528, 529, 530, 532, 544, 545, 546, 548, 0, 1, 2, 4, 8, 9, 10, 12, 16, 17, 18, 20, 32, 33, 34, 36, 64, 65, 66, 68, 72, 73, 74, 76, 80, 81, 82, 84, 96, 97, 98, 100, 128, 129, 130, 132, 136, 137, 138, 140, 144, 145, 146, 148, 160, 161, 162, 164, 256, 257, 258, 260, 264, 265, 266, 268, 272, 273, 274, 276, 288, 289, 290, 292, 512, 513, 514, 516, 520, 521, 522, 524, 528, 529, 530, 532, 544, 545, 546, 548, 0, 1, 2, 4, 8, 9, 10, 12, 16, 17, 18, 20, 32, 33, 34, 36, 64, 65, 66, 68, 72, 73, 74, 76, 80, 81, 82, 84, 96, 97, 98, 100, 128, 129, 130, 132, 136, 137, 138, 140, 144, 145, 146, 148, 160, 161, 162, 164, 256, 257, 258, 260, 264, 265, 266, 268, 272, 273, 274, 276, 288, 289, 290, 292, 512, 513, 514, 516, 520, 521, 522, 524, 528, 529, 530, 532, 544, 545, 546, 548, 0, 1, 2, 4, 8, 9, 10, 12, 16, 17, 18, 20, 32, 33, 34, 36, 64, 65, 66, 68, 72, 73, 74, 76, 80, 81, 82, 84, 96, 97, 98, 100, 128, 129, 130, 132, 136, 137, 138, 140, 144, 145, 146, 148, 160, 161, 162, 164, 256, 257, 258, 260, 264, 265, 266, 268, 272, 273, 274, 276, 288, 289, 290, 292, 512, 513, 514, 516, 520, 521, 522, 524, 528, 529, 530, 532, 544, 545, 546, 548, 0, 1, 2, 4, 8, 9, 10, 12, 16, 17, 18, 20, 32, 33, 34, 36, 64, 65, 66, 68, 72, 73, 74, 76, 80, 81, 82, 84, 96, 97, 98, 100, 128, 129, 130, 132, 136, 137, 138, 140, 144, 145, 146, 148, 160, 161, 162, 164, 256, 257, 258, 260, 264, 265, 266, 268, 272, 273, 274, 276, 288, 289, 290, 292, 512, 513, 514, 516, 520, 521, 522, 524, 528, 529, 530, 532, 544, 545, 546, 548, 0, 1, 2, 4, 8, 9, 10, 12, 16, 17, 18, 20, 32, 33, 34, 36, 64, 65, 66, 68, 72, 73, 74, 76, 80, 81, 82, 84, 96, 97, 98, 100, 128, 129, 130, 132, 136, 137, 138, 140, 144, 145, 146, 148, 160, 161, 162, 164, 256, 257, 258, 260, 264, 265, 266, 268, 272, 273, 274, 276, 288, 289, 290, 292, 512, 513, 514, 516, 520, 521, 522, 524, 528, 529, 530, 532, 544, 545, 546, 548, 0, 1, 2, 4, 8, 9, 10, 12, 16, 17, 18, 20, 32, 33, 34, 36, 64, 65, 66, 68, 72, 73, 74, 76, 80, 81, 82, 84, 96, 97, 98, 100, 128, 129, 130, 132, 136, 137, 138, 140, 144, 145, 146, 148, 160, 161, 162, 164, 256, 257, 258, 260, 264, 265, 266, 268, 272, 273, 274, 276, 288, 289, 290, 292, 512, 513, 514, 516, 520, 521, 522, 524, 528, 529, 530, 532, 544, 545, 546, 548, 0, 1, 2, 4, 8, 9, 10, 12, 16, 17, 18, 20, 32, 33, 34, 36, 64, 65, 66, 68, 72, 73, 74, 76, 80, 81, 82, 84, 96, 97, 98, 100, 128, 129, 130, 132, 136, 137, 138, 140]\n"
     ]
    }
   ],
   "source": [
    "encodings=[0]*1000\n",
    "j = 1\n",
    "for i in range(13):\n",
    "    if i not in [0,4,8]:\n",
    "        for w in wine_groups_for_virtual_mice[i]:\n",
    "            encodings[w]|=j\n",
    "        j<<=1\n",
    "print(encodings)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "wine_groups_for_real_mice=[ set() if i in [0,4,8] else wine_groups_for_virtual_mice[i] for i in range(13)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def test_result(poison_wine):\n",
    "    return [bool(poison_wine&w) for w in wine_groups_for_real_mice]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def make_decision(result):\n",
    "    r = result[:]\n",
    "    r[0] = sum(r[:4])<2\n",
    "    r[4] = sum(r[4:8])<2\n",
    "    r[8] = sum(r[8:])<2\n",
    "    g1, g2, g3 = set(), set(), set()\n",
    "    for i in range(4):\n",
    "        if r[i]:\n",
    "            g1 |= wine_groups_for_virtual_mice[i]\n",
    "    for i in range(4,8):\n",
    "        if r[i]:\n",
    "            g2 |= wine_groups_for_virtual_mice[i]\n",
    "    for i in range(8,13):\n",
    "        if r[i]:\n",
    "            g3 |= wine_groups_for_virtual_mice[i]\n",
    "    return g1 & g2 & g3\n",
    "\n",
    "def verify(poison_wine, decision):\n",
    "    return poison_wine <= decision\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0, 0)\n",
      "(10, 104)\n",
      "(20, 104)\n",
      "(30, 104)\n",
      "(40, 104)\n",
      "(50, 104)\n",
      "(60, 104)\n",
      "(70, 104)\n",
      "(80, 104)\n",
      "(90, 104)\n",
      "(100, 104)\n",
      "(110, 104)\n",
      "(120, 104)\n",
      "(130, 104)\n",
      "(140, 104)\n",
      "(150, 104)\n",
      "(160, 104)\n",
      "(170, 104)\n",
      "(180, 104)\n",
      "(190, 104)\n",
      "(200, 104)\n",
      "(210, 104)\n",
      "(220, 104)\n",
      "(230, 104)\n",
      "(240, 104)\n",
      "(250, 104)\n",
      "(260, 104)\n",
      "(270, 104)\n",
      "(280, 104)\n",
      "(290, 104)\n",
      "(300, 104)\n",
      "(310, 104)\n",
      "(320, 104)\n",
      "(330, 104)\n",
      "(340, 104)\n",
      "(350, 104)\n",
      "(360, 104)\n",
      "(370, 104)\n",
      "(380, 104)\n",
      "(390, 104)\n",
      "(400, 104)\n",
      "(410, 104)\n",
      "(420, 104)\n",
      "(430, 104)\n",
      "(440, 104)\n",
      "(450, 104)\n",
      "(460, 104)\n",
      "(470, 104)\n",
      "(480, 104)\n",
      "(490, 104)\n",
      "(500, 104)\n",
      "(510, 104)\n",
      "(520, 104)\n",
      "(530, 104)\n",
      "(540, 104)\n",
      "(550, 104)\n",
      "(560, 104)\n",
      "(570, 104)\n",
      "(580, 104)\n",
      "(590, 104)\n",
      "(600, 104)\n",
      "(610, 104)\n",
      "(620, 104)\n",
      "(630, 104)\n",
      "(640, 104)\n",
      "(650, 104)\n",
      "(660, 104)\n",
      "(670, 104)\n",
      "(680, 104)\n",
      "(690, 104)\n",
      "(700, 104)\n",
      "(710, 104)\n",
      "(720, 104)\n",
      "(730, 104)\n",
      "(740, 104)\n",
      "(750, 104)\n",
      "(760, 104)\n",
      "(770, 104)\n",
      "(780, 104)\n",
      "(790, 104)\n",
      "(800, 104)\n",
      "(810, 104)\n",
      "(820, 104)\n",
      "(830, 104)\n",
      "(840, 104)\n",
      "(850, 104)\n",
      "(860, 104)\n",
      "(870, 104)\n",
      "(880, 104)\n",
      "(890, 104)\n",
      "(900, 104)\n",
      "(910, 104)\n",
      "(920, 104)\n",
      "(930, 104)\n",
      "(940, 104)\n",
      "(950, 104)\n",
      "(960, 104)\n",
      "(970, 104)\n",
      "(980, 104)\n",
      "(990, 104)\n",
      "done\n"
     ]
    }
   ],
   "source": [
    "m = 0\n",
    "for i in range(999):\n",
    "    if i%10==0:\n",
    "        print(i,m)\n",
    "    for j in range(i,1000):\n",
    "        poison = {i,j}\n",
    "        result = test_result(poison)        \n",
    "        decision = make_decision(result)\n",
    "        if len(decision) > 104 or not verify(poison, decision):\n",
    "            print(i,j, len(decision))        \n",
    "            break\n",
    "        m = max(len(decision), m)\n",
    "print(\"done\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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