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#!/usr/bin/env perl

...
        }
    }
}

tr.pl : here are all the solutions:
1)5,2,2,2,2,2
...
10)2,2,2,2,2,5
11)5,5,5
12)2,2,2,2,7

        foreach(@$input){
                # added this to make sure that we have combinations ra
+ther than permutations:
                # see haukex's comment below
                next if( defined($v) && $_ < $v->{'number'} );
                ...