To find a subset of a set, having a specific sum, you can use this regex. It works for any set of non-negative integers.
sub subset_sum {
  my $targ = shift;
  my $re = join '', map '(' . '.' x $_ . ')?', @_;
  return
    map defined() ? length : (),
    (1 x $targ) =~ /^$re$/;
}

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