{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "load 'array-numbers.rb'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "38890"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ch = (0..9999).flat_map {|i| i.to_digits}\n",
    "ch.length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9, 7, 9, 9, 9, 8, 9, 9, 9, 9]"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ch[-10..-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ch[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ch[10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ch[100]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "38890"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ch.length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":champ"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def champ(i)\n",
    "  if i < 10\n",
    "    i\n",
    "  elsif i < 190\n",
    "    if (i - 10) % 2 == 0 # tens\n",
    "      ((i - 10) / 2) / 10 + 1\n",
    "    else # units\n",
    "      # ((i - 11) / 2) % 10\n",
    "     ((i - 10) / 2) % 10\n",
    "    end\n",
    "  elsif i < 2890\n",
    "    if (i - 190) % 3 == 0 #hundreds\n",
    "      ((i - 190) / 3) / 100 + 1\n",
    "    elsif (i - 190) % 3 == 1 # tens\n",
    "      (((i - 190) / 3) / 10) % 10\n",
    "    else # units\n",
    "      ((i - 190) / 3) % 10\n",
    "    end\n",
    "  elsif i < 38890\n",
    "    if (i - 2890) % 4 == 0 # thousands\n",
    "      ((i - 2890) / 4) / 1000 + 1\n",
    "    elsif (i - 2890) % 4 == 1 # hundreds\n",
    "      (((i - 2890) / 4) / 100) % 10\n",
    "    elsif (i - 2890) % 4 == 2 # tens\n",
    "      (((i - 2890) / 4) / 10) % 10\n",
    "    else # units\n",
    "      ((i - 2890) / 4) % 10\n",
    "    end\n",
    "  else\n",
    "    99\n",
    "  end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 :: 1 (2890)\n",
      "0 :: 0 (2891)\n",
      "0 :: 0 (2892)\n",
      "0 :: 0 (2893)\n",
      "1 :: 1 (2894)\n",
      "0 :: 0 (2895)\n",
      "0 :: 0 (2896)\n",
      "1 :: 1 (2897)\n",
      "1 :: 1 (2898)\n",
      "0 :: 0 (2899)\n",
      "0 :: 0 (2900)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2890..2900"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(2890..2900).each do |i|\n",
    "  puts \"#{champ i} :: #{ch[i]} (#{i})\"\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(1..38889).all? {|i| champ(i) == ch[i]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(1..38889).select {|i| champ(i) != ch[i]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "190 - 10 == 2 * 9 * 10 ** 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2890 - 190 == 3 * 9 * 10 ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "38890 - 2890 == 4 * 9 * 10 ** 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 10, 190, 2890, 38890, 488890, 5888890]"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# threshold, number of digits, offset\n",
    "(1..6).map {|n| n * 9 * 10**(n-1)}.reduce([1, 0, 0]) {|ss, n| ss + [[ss[-1][0] + n]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 0, 0, [9], [189], [2889], [38889], [488889], [5888889]]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(1..6).map {|n| n * 9 * 10**(n-1)}.reduce([[1, 0, 0]]) {|ss, n| ss + [[ss[-1][0] + n, n, ]]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0, 9], [1, 180], [2, 2700], [3, 36000], [4, 450000], [5, 5400000], [6, 63000000]]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(0..6).map {|n| [n, (n+1) * 9 * 10**n]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0, 1, 1], [9, 0, 10], [189, 1, 190], [2889, 2, 2890], [38889, 3, 38890], [488889, 4, 488890], [5888889, 5, 5888890], [68888889, 6, 68888890]]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(0..6).map {|n| [n, (n+1) * 9 * 10**n]}.reduce([[0, 1, 1]]) {|ts, ns| ts + [[ts[-1][0] + ns[1], ns[0], ts[-1][2] + ns[1]]] }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":champ2"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def champ2(n)\n",
    "  i = 1\n",
    "  limit = 10\n",
    "  offset = 0\n",
    "  while n >= limit\n",
    "    offset = limit\n",
    "    i += 1\n",
    "    step = i * 9 * 10**(i-1)\n",
    "    limit += step\n",
    "  end\n",
    "  unit = (n - offset) % i\n",
    "  digit = ((n - offset) / i) / (10 ** (i-(unit +1))) % 10\n",
    "  digit += 1 if unit == 0 && i != 1\n",
    "  # return i, limit, offset, unit, digit\n",
    "  digit\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 : 1 :: [1, 10, 0, 0, 1]\n",
      "2 : 2 :: [1, 10, 0, 0, 2]\n",
      "3 : 3 :: [1, 10, 0, 0, 3]\n",
      "4 : 4 :: [1, 10, 0, 0, 4]\n",
      "5 : 5 :: [1, 10, 0, 0, 5]\n",
      "6 : 6 :: [1, 10, 0, 0, 6]\n",
      "7 : 7 :: [1, 10, 0, 0, 7]\n",
      "8 : 8 :: [1, 10, 0, 0, 8]\n",
      "9 : 9 :: [1, 10, 0, 0, 9]\n",
      "10 : 1 :: [2, 190, 10, 0, 1]\n",
      "11 : 0 :: [2, 190, 10, 1, 0]\n",
      "12 : 1 :: [2, 190, 10, 0, 1]\n",
      "13 : 1 :: [2, 190, 10, 1, 1]\n",
      "14 : 1 :: [2, 190, 10, 0, 1]\n",
      "15 : 2 :: [2, 190, 10, 1, 2]\n",
      "16 : 1 :: [2, 190, 10, 0, 1]\n",
      "17 : 3 :: [2, 190, 10, 1, 3]\n",
      "18 : 1 :: [2, 190, 10, 0, 1]\n",
      "19 : 4 :: [2, 190, 10, 1, 4]\n",
      "20 : 1 :: [2, 190, 10, 0, 1]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1..20"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(1..20).each do |i| puts \"#{i} : #{champ i} :: #{champ2 i}\" end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "180 : 9 :: [2, 190, 10, 0, 9]\n",
      "181 : 5 :: [2, 190, 10, 1, 5]\n",
      "182 : 9 :: [2, 190, 10, 0, 9]\n",
      "183 : 6 :: [2, 190, 10, 1, 6]\n",
      "184 : 9 :: [2, 190, 10, 0, 9]\n",
      "185 : 7 :: [2, 190, 10, 1, 7]\n",
      "186 : 9 :: [2, 190, 10, 0, 9]\n",
      "187 : 8 :: [2, 190, 10, 1, 8]\n",
      "188 : 9 :: [2, 190, 10, 0, 9]\n",
      "189 : 9 :: [2, 190, 10, 1, 9]\n",
      "190 : 1 :: [3, 2890, 190, 0, 1]\n",
      "191 : 0 :: [3, 2890, 190, 1, 0]\n",
      "192 : 0 :: [3, 2890, 190, 2, 0]\n",
      "193 : 1 :: [3, 2890, 190, 0, 1]\n",
      "194 : 0 :: [3, 2890, 190, 1, 0]\n",
      "195 : 1 :: [3, 2890, 190, 2, 1]\n",
      "196 : 1 :: [3, 2890, 190, 0, 1]\n",
      "197 : 0 :: [3, 2890, 190, 1, 0]\n",
      "198 : 2 :: [3, 2890, 190, 2, 2]\n",
      "199 : 1 :: [3, 2890, 190, 0, 1]\n",
      "200 : 0 :: [3, 2890, 190, 1, 0]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "180..200"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(180..200).each do |i| puts \"#{i} : #{champ i} :: #{champ2 i}\" end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2880 : 6 :: [3, 2890, 190, 2, 6]\n",
      "2881 : 9 :: [3, 2890, 190, 0, 9]\n",
      "2882 : 9 :: [3, 2890, 190, 1, 9]\n",
      "2883 : 7 :: [3, 2890, 190, 2, 7]\n",
      "2884 : 9 :: [3, 2890, 190, 0, 9]\n",
      "2885 : 9 :: [3, 2890, 190, 1, 9]\n",
      "2886 : 8 :: [3, 2890, 190, 2, 8]\n",
      "2887 : 9 :: [3, 2890, 190, 0, 9]\n",
      "2888 : 9 :: [3, 2890, 190, 1, 9]\n",
      "2889 : 9 :: [3, 2890, 190, 2, 9]\n",
      "2890 : 1 :: [4, 38890, 2890, 0, 1]\n",
      "2891 : 0 :: [4, 38890, 2890, 1, 0]\n",
      "2892 : 0 :: [4, 38890, 2890, 2, 0]\n",
      "2893 : 0 :: [4, 38890, 2890, 3, 0]\n",
      "2894 : 1 :: [4, 38890, 2890, 0, 1]\n",
      "2895 : 0 :: [4, 38890, 2890, 1, 0]\n",
      "2896 : 0 :: [4, 38890, 2890, 2, 0]\n",
      "2897 : 1 :: [4, 38890, 2890, 3, 1]\n",
      "2898 : 1 :: [4, 38890, 2890, 0, 1]\n",
      "2899 : 0 :: [4, 38890, 2890, 1, 0]\n",
      "2900 : 0 :: [4, 38890, 2890, 2, 0]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2880..2900"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(2880..2900).each do |i| puts \"#{i} : #{champ i} :: #{champ2 i}\" end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(1..38889).all? {|i| champ2(i) == ch[i]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "210"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(0..6).map {|e| champ2(10**e)}.reduce(:*)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
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   "language": "ruby",
   "name": "ruby"
  },
  "language_info": {
   "file_extension": ".rb",
   "mimetype": "application/x-ruby",
   "name": "ruby",
   "version": "2.4.0"
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 },
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