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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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