{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":pentagonal"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def pentagonal(n)\n",
    "  n * (3 * n - 1) / 2\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2167, 1020 -> 5482660\n",
      "2167, 1020 -> 5482660\n"
     ]
    }
   ],
   "source": [
    "pentagonals = Set.new()\n",
    "\n",
    "found = false\n",
    "sum_index = 1\n",
    "best_k = 0\n",
    "best_j = 0\n",
    "best_diff = pentagonal(5000)\n",
    "\n",
    "while !found do\n",
    "  pentagonals << pentagonal(sum_index)\n",
    "  ((sum_index/2)...sum_index).each do |j|\n",
    "    k = sum_index - j\n",
    "    diff = pentagonal(j) - pentagonal(k)\n",
    "    if pentagonals.include?(diff) && pentagonals.include?(pentagonal(j)+pentagonal(k))\n",
    "      found = true\n",
    "      puts \"#{j}, #{k} -> #{diff}\"\n",
    "      if diff < best_diff\n",
    "        best_diff = diff\n",
    "        best_k = k\n",
    "        best_j = j\n",
    "      end\n",
    "    end\n",
    "  end\n",
    "  sum_index += 1\n",
    "end\n",
    "puts \"#{best_j}, #{best_k} -> #{best_diff}\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pentagonals.include?(pentagonal(2167))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "210"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pentagonal(12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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