41 lines
1.3 KiB
Factor
41 lines
1.3 KiB
Factor
! Copyright (c) 2008 Aaron Schaefer.
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! See http://factorcode.org/license.txt for BSD license.
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USING: kernel math.combinatorics math.parser math.primes sequences ;
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IN: project-euler.041
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! http://projecteuler.net/index.php?section=problems&id=41
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! DESCRIPTION
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! -----------
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! We shall say that an n-digit number is pandigital if it makes use of all the
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! digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is
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! also prime.
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! What is the largest n-digit pandigital prime that exists?
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! SOLUTION
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! --------
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! Check 7-digit pandigitals because if the sum of the digits in any number add
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! up to a multiple of three, then it is a multiple of three and can't be prime.
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! I assumed there would be a 7-digit answer, but technically a higher 4-digit
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! pandigital than the one given in the description was also possible.
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! 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
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! 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36
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! 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28 *** not divisible by 3 ***
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! 1 + 2 + 3 + 4 + 5 + 6 = 21
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! 1 + 2 + 3 + 4 + 5 = 15
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! 1 + 2 + 3 + 4 = 10 *** not divisible by 3 ***
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: euler041 ( -- answer )
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{ 7 6 5 4 3 2 1 } all-permutations
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[ 10 digits>integer ] map [ prime? ] find nip ;
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! [ euler041 ] 100 ave-time
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! 64 ms ave run time - 4.22 SD (100 trials)
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MAIN: euler041
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