Problem 1: The problem implies but does not actually state that all cards, by definition, have letters on one side and numbers on the other. If this is true then we need only turn over two cards, the 'A' and the '3'. If it were possible for a card to have letters on both sides we would also have to turn over the 'B' as well (since an A on one side and a B on the other would violate the rule). Incidentally, Cliff and I talked about this problem, so my answer doesn't really count for "scoring" purposes.

Problem 2: We can't decide whether all, some, or none of the archeologists are chess players. As far as I can see, all we can conclude are the rather trivial observations that: 1) None of the biologists is an archeologist, and 2) Some of the chess players are biologists.

Well, Cliff, what do you say?