I think that the intent of the puzzle is that if black's last move was g7-g5, white mates by ph5xg6 (en passant), threatening Rd8 mate, and if black castles, white mates with h6-h7, while if black's last move was with the king or rook, white plays Ke6, with an unstoppable threat of Rd8 mate, since black, having moved the king or rook, cannot castle. So white has a move that mates in two, but doesn't know what the move is without knowing the history of the game to this point. But I'm missing a step; If black's last move was g6-g5, I can't see a proof that black can't castle, so I can't find a mate. White's move before that might have been, for example, RxQd4, and black's move before that was Qd4. The white pawn on h6 could have gotten there from g5 long ago, capturing a knight, before black moved g7-g6. What am I missing? Andy Latto On Sat, May 27, 2017 at 2:03 PM, <rcs@xmission.com> wrote:

[from Eric Angelini -- Rich]

------------ Date: Tue, 23 May 2017 11:36:01 +0200 Subject: Chess weirdness From: Eric Angelini <Eric.Angelini@kntv.be>

Hello math-fun, Here is the chess problem I was mentioning in my last post:

+---+---+---+---+---+---+---+---+ | | | | | k | | | r | 8 +---+---+---+---+---+---+---+---+ | | | | | | | | | 7 +---+---+---+---+---+---+---+---+ | | | | | | B | | P | 6 +---+---+---+---+---+---+---+---+ | | | | R | | K | p | P | 5 +---+---+---+---+---+---+---+---+ | | | | | | | | | 4 +---+---+---+---+---+---+---+---+ | | | | | | | | | 3 +---+---+---+---+---+---+---+---+ | | | | | | | | | 2 +---+---+---+---+---+---+---+---+ | | | | | | | | | 1 +---+---+---+---+---+---+---+---+ a b c d e f g h

White to move; mate in 2

The "problem" is that there is -- and there is no mate in 2! Kind of a 2-states quantum superposition! If you had the White pieces, what would your first move be?

Best, É.

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-- Andy.Latto@pobox.com