47 lines
1.1 KiB
Factor
47 lines
1.1 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 math.functions math.ranges project-euler.common sequences ;
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IN: project-euler.030
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! http://projecteuler.net/index.php?section=problems&id=30
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! DESCRIPTION
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! -----------
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! Surprisingly there are only three numbers that can be written as the sum of
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! fourth powers of their digits:
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! 1634 = 1^4 + 6^4 + 3^4 + 4^4
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! 8208 = 8^4 + 2^4 + 0^4 + 8^4
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! 9474 = 9^4 + 4^4 + 7^4 + 4^4
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! As 1 = 1^4 is not a sum it is not included.
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! The sum of these numbers is 1634 + 8208 + 9474 = 19316.
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! Find the sum of all the numbers that can be written as the sum of fifth
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! powers of their digits.
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! SOLUTION
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! --------
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! if n is the number of digits
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! n * 9^5 = 10^n when n ≈ 5.513
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! 10^5.513 ≈ 325537
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<PRIVATE
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: sum-fifth-powers ( n -- sum )
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number>digits [ 5 ^ ] map-sum ;
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PRIVATE>
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: euler030 ( -- answer )
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325537 <iota> [ dup sum-fifth-powers = ] filter sum 1 - ;
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! [ euler030 ] 100 ave-time
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! 1700 ms ave run time - 64.84 SD (100 trials)
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SOLUTION: euler030
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