{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "require 'set'\n",
    "require 'awesome_print'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits = (1..9).to_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":full_subbags"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "class Array\n",
    "  def subbags(n)\n",
    "    return enum_for(:subbags, n) unless block_given?\n",
    "    if n == 1\n",
    "      yield [self]\n",
    "    else\n",
    "      (0..self.length).each do |i|\n",
    "        self.combination(i).each do |f|\n",
    "          (self - f).subbags(n-1).each do |r|\n",
    "            yield [f] + r\n",
    "          end\n",
    "        end\n",
    "      end\n",
    "    end\n",
    "  end\n",
    "  \n",
    "  def full_subbags(n)\n",
    "    return enum_for(:full_subbags, n) unless block_given?\n",
    "    self.subbags(n).select {|bags| bags.none? {|b| b.empty?}}.each do |bs|\n",
    "      yield bs\n",
    "    end\n",
    "  end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1, 2, 3]]\n"
     ]
    }
   ],
   "source": [
    "[1,2,3].subbags(1) {|i| puts i}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[[1, 2, 3]]]"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[1,2,3].subbags(1).to_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[], [1, 2, 3]]\n",
      "[[1], [2, 3]]\n",
      "[[2], [1, 3]]\n",
      "[[3], [1, 2]]\n",
      "[[1, 2], [3]]\n",
      "[[1, 3], [2]]\n",
      "[[2, 3], [1]]\n",
      "[[1, 2, 3], []]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0..3"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[1,2,3].subbags(2) {|i| puts i}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[[], [1, 2, 3]], [[1], [2, 3]], [[2], [1, 3]], [[3], [1, 2]], [[1, 2], [3]], [[1, 3], [2]], [[2, 3], [1]], [[1, 2, 3], []]]"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[1,2,3].subbags(2).to_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[1,2,3].subbags(2).to_a.length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[[], [], [1, 2, 3]], [[], [1], [2, 3]], [[], [2], [1, 3]], [[], [3], [1, 2]], [[], [1, 2], [3]], [[], [1, 3], [2]], [[], [2, 3], [1]], [[], [1, 2, 3], []], [[1], [], [2, 3]], [[1], [2], [3]], [[1], [3], [2]], [[1], [2, 3], []], [[2], [], [1, 3]], [[2], [1], [3]], [[2], [3], [1]], [[2], [1, 3], []], [[3], [], [1, 2]], [[3], [1], [2]], [[3], [2], [1]], [[3], [1, 2], []], [[1, 2], [], [3]], [[1, 2], [3], []], [[1, 3], [], [2]], [[1, 3], [2], []], [[2, 3], [], [1]], [[2, 3], [1], []], [[1, 2, 3], [], []]]"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[1,2,3].subbags(3).to_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "27"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[1,2,3].subbags(3).to_a.length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i: 0, f: []\n",
      "i: 1, f: [1]\n",
      "i: 1, f: [2]\n",
      "i: 1, f: [3]\n",
      "i: 2, f: [1, 2]\n",
      "i: 2, f: [1, 3]\n",
      "i: 2, f: [2, 3]\n",
      "i: 3, f: [1, 2, 3]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0..3"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(0..[1,2,3].length).each do |i|\n",
    "  [1,2,3].combination(i).each do |f|\n",
    "    puts \"i: #{i}, f: #{f}\"\n",
    "  end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[[1], [2], [3, 4]], [[1], [3], [2, 4]], [[1], [4], [2, 3]], [[1], [2, 3], [4]], [[1], [2, 4], [3]], [[1], [3, 4], [2]], [[2], [1], [3, 4]], [[2], [3], [1, 4]], [[2], [4], [1, 3]], [[2], [1, 3], [4]], [[2], [1, 4], [3]], [[2], [3, 4], [1]], [[3], [1], [2, 4]], [[3], [2], [1, 4]], [[3], [4], [1, 2]], [[3], [1, 2], [4]], [[3], [1, 4], [2]], [[3], [2, 4], [1]], [[4], [1], [2, 3]], [[4], [2], [1, 3]], [[4], [3], [1, 2]], [[4], [1, 2], [3]], [[4], [1, 3], [2]], [[4], [2, 3], [1]], [[1, 2], [3], [4]], [[1, 2], [4], [3]], [[1, 3], [2], [4]], [[1, 3], [4], [2]], [[1, 4], [2], [3]], [[1, 4], [3], [2]], [[2, 3], [1], [4]], [[2, 3], [4], [1]], [[2, 4], [1], [3]], [[2, 4], [3], [1]], [[3, 4], [1], [2]], [[3, 4], [2], [1]]]"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[1,2,3,4].full_subbags(3).to_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "18150"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.full_subbags(3).to_a.length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":euler_product"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def euler_product(subbags)\n",
    "  products = []\n",
    "  a, b, c = subbags\n",
    "  csort = c.sort\n",
    "  a.permutation.each do |ap|\n",
    "    an = ap.map {|d| d.to_s}.join.to_i\n",
    "    b.permutation.each do |bp|\n",
    "      bn = bp.map {|d| d.to_s}.join.to_i\n",
    "      cn = (an * bn)\n",
    "      cp = cn.to_s.split('').map {|d| d.to_i}\n",
    "      if cp.sort == csort\n",
    "        products << cn\n",
    "      end\n",
    "    end\n",
    "  end\n",
    "  products\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "123"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[1,2,3].map {|d| d.to_s}.join.to_i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "123.to_s.split('').map {|d| d.to_i}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[1,2,3,4].full_subbags(3).flat_map {|bs| euler_product bs}.to_set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[7254]"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "euler_product([[3, 9], [1, 8, 6], [7, 2, 5, 4]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "45228"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.full_subbags(3).flat_map {|bs| euler_product bs}.to_set.sum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Ruby 2.4.0",
   "language": "ruby",
   "name": "ruby"
  },
  "language_info": {
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   "mimetype": "application/x-ruby",
   "name": "ruby",
   "version": "2.4.0"
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