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Solution to Project Euler problem 41

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Aaron Schaefer 2008-02-03 16:15:03 -05:00
parent 1954114d85
commit 4a0bb3b032
2 changed files with 42 additions and 2 deletions
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! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: kernel math.combinatorics math.parser math.primes sequences ;
IN: project-euler.041
! http://projecteuler.net/index.php?section=problems&id=41
! DESCRIPTION
! -----------
! 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.
! What is the largest n-digit pandigital prime that exists?
! SOLUTION
! --------
! Check 7-digit pandigitals because if the sum of the digits in any number add
! up to a multiple of three, then it is a multiple of three and can't be prime.
! I assumed there would be a 7-digit answer, but technically a higher 4-digit
! pandigital than the one given in the description was also possible.
! 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
! 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36
! 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28 *** not divisible by 3 ***
! 1 + 2 + 3 + 4 + 5 + 6 = 21
! 1 + 2 + 3 + 4 + 5 = 15
! 1 + 2 + 3 + 4 = 10 *** not divisible by 3 ***
: euler041 ( -- answer )
{ 7 6 5 4 3 2 1 } all-permutations
[ 10 swap digits>integer ] map [ prime? ] find nip ;
! [ euler041 ] 100 ave-time
! 107 ms run / 7 ms GC ave time - 100 trials
MAIN: euler041

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project-euler.029 project-euler.030 project-euler.031 project-euler.032 project-euler.029 project-euler.030 project-euler.031 project-euler.032
project-euler.033 project-euler.034 project-euler.035 project-euler.036 project-euler.033 project-euler.034 project-euler.035 project-euler.036
project-euler.037 project-euler.038 project-euler.039 project-euler.040 project-euler.037 project-euler.038 project-euler.039 project-euler.040
project-euler.048 project-euler.067 project-euler.075 project-euler.134 project-euler.041 project-euler.048 project-euler.067 project-euler.075
project-euler.169 project-euler.173 project-euler.175 ; project-euler.134 project-euler.169 project-euler.173 project-euler.175 ;
IN: project-euler IN: project-euler
<PRIVATE <PRIVATE