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merlyn wrote: All you need is a good generating algorithm and you can brute force this!

I thought this idea was so intensely cool that I just had to try it out. However, coming up with a "good generating alorithm" escapes me. First, I took the list of possible permutations that dws created and translated it:

```
[1][2][3][4,5,6]
1  1  1  0 0
[1][2][3,4][5,6]
1  1  0 1  0
[1][2][3,4,5][6]
1  1  0 0 1
[1][2,3][4][5,6]
1  0 1  1  0
[1][2,3][4,5][6]
1  0 1  0 1
[1][2,3,4][5][6]
1  0 0 1  1
[1,2][3][4][5,6]
0 1  1  1  0
[1,2][3][4,5][6]
0 1  1  0 1
[1,2][3,4][5][6]
0 1  0 1  1
[1,2,3][4][5][6]
0 0 1  1  1

Then, once I was sure I understood it, I went ahead and hardcoded that so I could manipulate it and look for patterns.

```#!/usr/bin/perl -w
use strict;
use Data::Dumper;

my @categories = qw/
11100
11010
11001
10110
10101
10011
01110
01101
01011
00111
/;

@categories = sort @categories;
my @cat2 =
sort { \$a <=> \$b }
map  { ord pack 'b*', \$_ }
@categories;

print Dumper \@categories, \@cat2;

Which prints the following:

```\$VAR1 = [
'00111',
'01011',
'01101',
'01110',
'10011',
'10101',
'10110',
'11001',
'11010',
'11100'
];
\$VAR2 = [
7,
11,
13,
14,
19,
21,
22,
25,
26,
28
];

Needless to say, the list seems arbitrary (even though we know it's not) and try as I might, I can't come up with a method of creating that, much less writing a generalized routine. I thought about trying to discover a pattern in the sequences, but no dice. Later, I tried creating a "picture" of the bits and swapping pairs, but I couldn't come up with a sequence for that, either. I'll start looking into permutators, but I feel like I'm missing something awfully basic here. There are only 10 possible combinations, so I didn't think generating them would be that hard :(

Cheers,
Ovid

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In reply to Re: •Re: Puzzle: need a more general algorithm by Ovid
in thread Puzzle: need a more general algorithm by Ovid

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