Good turnout today - eleven. We had a quick lesson on checkmate with just a king and queen, or just a King and Rook. Often stalemates result from carelessness on the part of the players who is ahead, but sometimes a clever move by the person who is behind can force a stalemate. 

What is Black's best move?

Problem #2 Harder. Again, what is Black's best move?

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Answers: Problem #1. Bg3+ forces either a stalemate if the Bishop is taken (by either piece) or a draw due to insufficient material if the King flees allowing you to capture his queen.

Problem #2. Rxg3+ White cannot capture because of stalemate, so he must play Kh2, but now Rg2+. White cannot capture, but then he cannot get out of check, so the game is a draw.