I would argue that the goal behind the mathematics (and you have your rules down, if not the terminology) is to come up with a set of "words" that satisfy the hints. This narrows the searchspace down dramatically. Then, it's a matter of a simple anagram-matching program (which is a lot quicker than the programs that were discussed here) to find the correct word(s).
Being right, does not endow the right to be rude; politeness costs nothing.
Being unknowing, is not the same as being stupid.
Expressing a contrary opinion, whether to the individual or the group, is more often a sign of deeper thought than of cantankerous belligerence.
Do not mistake your goals as the only goals; your opinion as the only opinion; your confidence as correctness. Saying you know better is not the same as explaining you know better.
