euler41.ipynb

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  21    "source": [
  22     "load 'primes.rb'\n",
  23     "load 'array-numbers.rb'"
  24    ]
  25   },
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  36        ":pandigital?"
  37       ]
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  45     "class Integer\n",
  46     "  def pandigital?\n",
  47     "    self.to_digits.sort == (1..Math.log10(self).ceil).to_a\n",
  48     "  end\n",
  49     "end"
  50    ]
  51   },
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  70    "source": [
  71     "Math.log10(21).ceil"
  72    ]
  73   },
  74   {
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  76    "execution_count": 13,
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  81     {
  82      "data": {
  83       "text/plain": [
  84        "[[12, [1, 2], [1, 2]], [21, [1, 2], [1, 2]], [123, [1, 2, 3], [1, 2, 3]], [132, [1, 2, 3], [1, 2, 3]], [213, [1, 2, 3], [1, 2, 3]], [231, [1, 2, 3], [1, 2, 3]], [312, [1, 2, 3], [1, 2, 3]], [321, [1, 2, 3], [1, 2, 3]], [1234, [1, 2, 3, 4], [1, 2, 3, 4]], [1243, [1, 2, 3, 4], [1, 2, 3, 4]], [1324, [1, 2, 3, 4], [1, 2, 3, 4]], [1342, [1, 2, 3, 4], [1, 2, 3, 4]], [1423, [1, 2, 3, 4], [1, 2, 3, 4]], [1432, [1, 2, 3, 4], [1, 2, 3, 4]]]"
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  87      "execution_count": 13,
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  92    "source": [
  93     "(1..2000).map {|i| [i, i.to_digits.sort, (1..Math.log10(i).ceil).to_a]}.select {|i, ds, ms| ds == ms}"
  94    ]
  95   },
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 114    "source": [
 115     "13.pandigital?"
 116    ]
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 120    "metadata": {},
 121    "source": [
 122     "# Divisibility rule\n",
 123     "A number is divisible by 3 iff the sum of its digits is divisible by 3. Therefore, all pandigital numbers, apart from those to 4 and 7, are composite. \n",
 124     "\n",
 125     "Therefore, we check just the seven digit primes first."
 126    ]
 127   },
 128   {
 129    "cell_type": "code",
 130    "execution_count": 30,
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 138        "7652413"
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 141      "execution_count": 30,
 142      "metadata": {},
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 145    ],
 146    "source": [
 147     "(1..7).to_a.permutation.select {|ds| ds.to_i.prime?}.map {|ds| ds.to_i}.max"
 148    ]
 149   },
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