44 lines
1.1 KiB
Ruby
44 lines
1.1 KiB
Ruby
descr=%{
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We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.
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What is the largest n-digit pandigital prime that exists?
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}
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thoughts=%{
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remark that all 9-digit pandigital number are not prime.
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1 + ... + 9 = 45 which is divisible by 3
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We don't need to search for prime pandigital superior to 10**8
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Also
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1 = 1
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1+2 = 3 => divisible by 3
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1+2+3 = 6 => divisible by 3
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1+2+3+4 = 10
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1+2+3+4+5 = 15 => divisible by 3
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1+ ... +6 = 21 => divisible by 3
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1+ ... +7 = 28
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1+ ... +8 = 36 => divisible by 3
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1+ ... +9 = 45 => divisible by 3
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Therefore at max there exists a 7-digit pandigital prime
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if not only a 4-digit pandigital prime
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}
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puts "Read primes"
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primes=File.read("firsts_10MM_primes.txt").split()
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$numbers=%q(1234567).split('').sort
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def is_pandigital(str)
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return str.split('').sort == $numbers
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end
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puts "Search pandigitals"
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primes.each do |str|
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next if str.length != 7
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if is_pandigital(str)
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puts str
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end
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end
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