euler44.ipynb

   1 {
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   9    "outputs": [
  10     {
  11      "data": {
  12       "text/plain": [
  13        ":pentagonal"
  14       ]
  15      },
  16      "execution_count": 2,
  17      "metadata": {},
  18      "output_type": "execute_result"
  19     }
  20    ],
  21    "source": [
  22     "def pentagonal(n)\n",
  23     "  n * (3 * n - 1) / 2\n",
  24     "end"
  25    ]
  26   },
  27   {
  28    "cell_type": "code",
  29    "execution_count": 22,
  30    "metadata": {
  31     "collapsed": false
  32    },
  33    "outputs": [
  34     {
  35      "name": "stdout",
  36      "output_type": "stream",
  37      "text": [
  38       "2167, 1020 -> 5482660\n",
  39       "2167, 1020 -> 5482660\n"
  40      ]
  41     }
  42    ],
  43    "source": [
  44     "pentagonals = Set.new()\n",
  45     "\n",
  46     "found = false\n",
  47     "sum_index = 1\n",
  48     "best_k = 0\n",
  49     "best_j = 0\n",
  50     "best_diff = pentagonal(5000)\n",
  51     "\n",
  52     "while !found do\n",
  53     "  pentagonals << pentagonal(sum_index)\n",
  54     "  ((sum_index/2)...sum_index).each do |j|\n",
  55     "    k = sum_index - j\n",
  56     "    diff = pentagonal(j) - pentagonal(k)\n",
  57     "    if pentagonals.include?(diff) && pentagonals.include?(pentagonal(j)+pentagonal(k))\n",
  58     "      found = true\n",
  59     "      puts \"#{j}, #{k} -> #{diff}\"\n",
  60     "      if diff < best_diff\n",
  61     "        best_diff = diff\n",
  62     "        best_k = k\n",
  63     "        best_j = j\n",
  64     "      end\n",
  65     "    end\n",
  66     "  end\n",
  67     "  sum_index += 1\n",
  68     "end\n",
  69     "puts \"#{best_j}, #{best_k} -> #{best_diff}\""
  70    ]
  71   },
  72   {
  73    "cell_type": "code",
  74    "execution_count": 18,
  75    "metadata": {
  76     "collapsed": false
  77    },
  78    "outputs": [
  79     {
  80      "data": {
  81       "text/plain": [
  82        "true"
  83       ]
  84      },
  85      "execution_count": 18,
  86      "metadata": {},
  87      "output_type": "execute_result"
  88     }
  89    ],
  90    "source": [
  91     "pentagonals.include?(pentagonal(2167))"
  92    ]
  93   },
  94   {
  95    "cell_type": "code",
  96    "execution_count": 23,
  97    "metadata": {
  98     "collapsed": false
  99    },
 100    "outputs": [
 101     {
 102      "data": {
 103       "text/plain": [
 104        "210"
 105       ]
 106      },
 107      "execution_count": 23,
 108      "metadata": {},
 109      "output_type": "execute_result"
 110     }
 111    ],
 112    "source": [
 113     "pentagonal(12)"
 114    ]
 115   },
 116   {
 117    "cell_type": "code",
 118    "execution_count": null,
 119    "metadata": {
 120     "collapsed": true
 121    },
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 124   }
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 141 }