2008-02-08 17:27:42 -05:00
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! Copyright (c) 2008 Aaron Schaefer.
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! See http://factorcode.org/license.txt for BSD license.
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2008-07-03 16:34:58 -04:00
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USING: kernel math math.combinatorics math.ranges sequences ;
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2008-02-08 17:27:42 -05:00
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IN: project-euler.053
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! http://projecteuler.net/index.php?section=problems&id=53
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! DESCRIPTION
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! -----------
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! There are exactly ten ways of selecting three from five, 12345:
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! 123, 124, 125, 134, 135, 145, 234, 235, 245, and 345
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! In combinatorics, we use the notation, 5C3 = 10.
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! In general,
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! nCr = n! / r! * (n - r)!
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! where r ≤ n, n! = n * (n − 1) * ... * 3 * 2 * 1, and 0! = 1.
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! It is not until n = 23, that a value exceeds one-million: 23C10 = 1144066.
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! How many values of nCr, for 1 ≤ n ≤ 100, are greater than one-million?
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! SOLUTION
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! --------
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: euler053 ( -- answer )
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2008-02-08 20:43:44 -05:00
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23 100 [a,b] [ dup [ nCk 1000000 > ] with count ] sigma ;
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2008-02-08 17:27:42 -05:00
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! [ euler053 ] 100 ave-time
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! 64 ms run / 2 ms GC ave time - 100 trials
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MAIN: euler053
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