Since I don't see the glob trick mentioned in this thread, and I'm not too keen on your pick-random-combos-until-we-think-weve-got-them-all solution, here are two ways to solve the locker combo problem.

#!/usr/bin/perl -wT
use strict;

# golfed version using glob
my $nums = join(',',1..31);
my @list1 = glob("{$nums}-{$nums}-{$nums}");
print "L1: $_\n" for @list1;

# more sane way of doing that.....
my @list2;
for my $i (1..31) {
  for my $j (1..31) {
    for my $k (1..31) {
      push(@list2,"$i-$j-$k");
    }
  }
}
print "L2: $_\n" for @list2;
[download]

And here is the glob trick used to solve the original problem...

#!/usr/bin/perl -wT
use strict;

# one ordering....
my $letters = ',A,C,G,N,T';
my @list1 = grep {/./} glob("{$letters}"x4);
print "L1: $_\n" for @list1;

# different ordering
my $letter2 = 'A,C,G,N,T';
my @list2 = (glob("{$letter2}"x2),glob("{$letter2}"x3),glob("{$letter2
+}"x4));
print "L2: $_\n" for @list2;
[download]

-Blake