Basic brute-force solution of solution to Siecherman Dice problem

siecherman.ipynb

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  "name": "Siecherman Dice"
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   "cells": [
    {
     "cell_type": "code",
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     "input": "import itertools\n\n# Generate distribution of real dice\nrealdice1 = [1, 2, 3, 4, 5, 6]\nrealdice2 = [1, 2, 3, 4, 5, 6]\n\nrealdist = {}\nfor x in realdice1:\n    for y in realdice2:\n        realdist[x+y]= realdist.get(x+y, 0)+1\n        \n        \n# testgrid(D1, D2)\n# Test two dice to see if the probability distribution of their \n# sum is the same as two standard dice\ndef testgrid(D1, D2):  \n    results = {}\n    for x in D1:\n        for y in D2:\n            results[x+y]= results.get(x+y, 0)+1\n            if results[x+y] > realdist.get(x+y, 99):\n                return False\n\n    for k in results:\n        if not (results[k] == realdist.get(k, -1)):\n            return False\n\n    return True\n\n\n# Test all combinations of dice.\n# (this was slow when I tried it on the train because I used wasn't thinking\n# and used itertools.product() instead of combinations_with_replacement();\n# itertools.product() returns every combination *and* permutation, so it takes forever.\nfor D1 in itertools.combinations_with_replacement([1, 2, 3, 4, 5, 6, 7, 8], 6):\n    for D2 in itertools.combinations_with_replacement([1, 2, 3, 4, 5, 6, 7, 8], 6):\n        if max(D1) + max(D2) > 12: continue\n        if testgrid(D1, D2):\n            print D1, D2",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "(1, 2, 2, 3, 3, 4) (1, 3, 4, 5, 6, 8)\n(1, 2, 3, 4, 5, 6)"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": " (1, 2, 3, 4, 5, 6)\n(1, 3, 4, 5, 6, 8)"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": " (1, 2, 2, 3, 3, 4)\n"
      }
     ],
     "prompt_number": 63
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": []
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