Done puzzle 49
[project-euler.git] / euler41.ipynb
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22 "load 'primes.rb'\n",
23 "load 'array-numbers.rb'"
24 ]
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36 ":pandigital?"
37 ]
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44 "source": [
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 ]
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62 "2"
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70 "source": [
71 "Math.log10(21).ceil"
72 ]
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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]]]"
85 ]
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93 "(1..2000).map {|i| [i, i.to_digits.sort, (1..Math.log10(i).ceil).to_a]}.select {|i, ds, ms| ds == ms}"
94 ]
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109 "execution_count": 19,
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114 "source": [
115 "13.pandigital?"
116 ]
117 },
118 {
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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 ]
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138 "7652413"
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146 "source": [
147 "(1..7).to_a.permutation.select {|ds| ds.to_i.prime?}.map {|ds| ds.to_i}.max"
148 ]
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150 {
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