{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "load 'primes.rb'\n",
    "load 'array-numbers.rb'\n",
    "primes = Primes.instance\n",
    "true"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":replace"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def replace(num, positions, replace_with)\n",
    "  digits = num.to_digits\n",
    "  positions.each do |p|\n",
    "    digits[p] = replace_with\n",
    "  end\n",
    "  digits.to_i\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "56993"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "replace(56003, [2, 3], 9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":replace_in_positions"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def replace_in_positions(num, positions)\n",
    "  (0..9).map {|d| replace num, positions, d}.select {|n| n.to_digits.length == num.to_digits.length}\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[56003, 56113, 56223, 56333, 56443, 56553, 56663, 56773, 56883, 56993]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "replace_in_positions(56003, [2, 3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":count_primes_in_positions"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def count_primes_in_positions(num, positions)\n",
    "  others = replace_in_positions(num, positions).select {|n| n.prime?}\n",
    "  if others.include?(num)\n",
    "    others.length\n",
    "  else\n",
    "    0\n",
    "  end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "count_primes_in_positions(56004, [2, 3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":best_count_primes_r"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def best_count_primes_r(num, n_digits)\n",
    "  possibles = (0...num.to_digits.length).to_a\n",
    "  possibles.combination(n_digits).map {|ps| count_primes_in_positions(num, ps)}.max\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_count_primes_r(56003, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_count_primes_r(3, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":best_count_primes"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def best_count_primes(num)\n",
    "  replacements = (1..num.to_digits.length).to_a\n",
    "  replacements.map {|n| best_count_primes_r(num, n)}.max\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_count_primes(56003)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_count_primes(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":sequence"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def sequence(&generator)\n",
    "  Enumerator.new do |yielder|\n",
    "    n = 0\n",
    "    loop do\n",
    "      yielder.yield generator.call(n)\n",
    "      n = n + 1\n",
    "    end\n",
    "  end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[2, 4], [3, 4], [5, 4], [7, 4], [11, 5], [13, 6], [17, 5], [19, 5], [23, 6], [29, 5], [31, 5], [37, 5], [41, 5], [43, 6], [47, 5], [53, 6], [59, 5], [61, 5], [67, 5], [71, 5]]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "primes.take(20).map {|p| [p, best_count_primes(p)]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "121313"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i = 1\n",
    "while best_count_primes(primes[i]) < 8 do\n",
    "  i += 1\n",
    "end\n",
    "primes[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_count_primes 120383"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[333383, 555383, 777383], [110183, 330383, 660683, 880883], [], [330383, 770387, 990389], [323383, 525583, 626683, 929983], [121313, 222323, 323333, 424343, 525353, 626363, 828383, 929393], [323383, 929389], [620663, 720773], [120181], [920399], [], [122323, 166363], [], [100003, 120223, 140443, 160663, 170773, 180883], [], [110311], [], [121181], [], []]"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num = 120383\n",
    "possibles = (0...num.to_digits.length).to_a\n",
    "possibles.combination(3).map {|ps| replace_in_positions(num, ps).select {|n| n.prime?}}# .map {|ps| count_primes_in_positions(num, ps)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_count_primes(121313)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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   "name": "ruby"
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