Solution to the Wife Puzzle

William's wife isn't Barbara, because the former gave the latter a permanent. William's wife must be either Gilda or Gloria.

Fred's wife isn't Gilda, because he speaks only Basque and her husband speaks only French. So Fred's wife is either Gloria or Barbara.

If John is bald, he doesn't live next door to Gilda and he doesn't speak Spanish and Basque.

Therefore, John must speak French and be married to Gilda. Only Gloria can be William's wife and the horrible cashmere shredder.

Evidence: This is what is left of the sweater!