#### /extra/project-euler/052/052.factor

http://github.com/abeaumont/factor
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``` 1! Copyright (c) 2008 Aaron Schaefer.
3USING: combinators.short-circuit kernel math math.functions
4    project-euler.common sequences sorting grouping ;
5IN: project-euler.052
6
7! http://projecteuler.net/index.php?section=problems&id=52
8
9! DESCRIPTION
10! -----------
11
12! It can be seen that the number, 125874, and its double, 251748, contain
13! exactly the same digits, but in a different order.
14
15! Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x,
16! contain the same digits.
17
18
19! SOLUTION
20! --------
21
22! Analysis shows the number must be odd, divisible by 3, and larger than 123456
23
24<PRIVATE
25
26: map-nx ( n x -- seq )
27    iota [ 1 + * ] with map ; inline
28
29: all-same-digits? ( seq -- ? )
30    [ number>digits natural-sort ] map all-equal? ;
31
32: candidate? ( n -- ? )
33    { [ odd? ] [ 3 divisor? ] } 1&& ;
34
35: next-all-same ( x n -- n )
36    dup candidate? [
37        2dup swap map-nx all-same-digits?
38        [ nip ] [ 1 + next-all-same ] if
39    ] [
40        1 + next-all-same
41    ] if ;
42
43PRIVATE>
44
45: euler052 ( -- answer )
46    6 123456 next-all-same ;
47
48! [ euler052 ] 100 ave-time
49! 92 ms ave run time - 6.29 SD (100 trials)
50
51SOLUTION: euler052
```