Here's my problem: say we have four sets of letters (abcdef) (abde) (abc) (ad). We can only add or subtract those sets in a way that (abc) + (ad) = (aabcd), (abcdef) - (abde) = (cf), but (abc) - (ad) is not allowed. Is it possible to get (b) only with these rules?
(inspired by a "find an area" geometry problem) (is there a tag for these specific types of problems?)
Expanding on my comment, once we see that we can't use (abcdef) at all, of the remaining sets (abc) is the only one that has a 'c', and (abde) is the only one that has an 'e', rendering both of those useless.
The remaining set is (ad) and obviously we can't get (b) by itself.