I've thought about this particular problem before, and I wrote the kind of program you would like to see, in C++. It was challenging, and somewhat time-consuming, which is probably why no one has responded yet like that; I was going to simply translate my program to Perl, but I think I dropped it in the bit bucket.

I eventually generalized the problem and solved it mathematically, noticing that 12 == (3**3 - 1)/2 - 1. Thus, to me, this is an old case of the following: given the task "write a program to sum the numbers from 1 to $x" after learning about loops, does one write print $x*($x+1)/2 or

for $i ( 1 .. $x ) {
  $sum += $i;
}
print $sum;
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So, I went the easier route and golfed in a relatively general way; my comparisons "2 9 11 12 <=> 3 5 6 8", etc., are not hard-coded (I could write a much shorter program otherwise) and the computation of the result is clever. I hope that this is okay. I understand your challenge, but I still think that the less-than-240-characters above is an accomplishment. Thank you for the clarification, though.