Knocked Off Piece

The following position occurs in a real game, right after one of the pieces gets knocked off the board. What was the piece?

It was a black knight. First, notice that the black pawns have moved 14 times diagonally and thus they have taken 14 pieces. Therefore the knocked off piece is black. Since it is impossible for both kings to be checked at the same time, the missing piece was positioned on a2. It couldn’t be a queen or a rook, because the white king would be checked both by it and the pawn on b3, which is impossible. Therefore the missing piece is either the black white-squared bishop or the black knight. However, the pawns on b7 and d7 haven’t been moved the entire game and then the black white-squared bishop hasn’t either. Thus we conclude that the knocked off piece is a black knight.

Missing Pawns

White to play and mate in 4 moves.

Remark: The position on the diagram is one which occurs in actual play.

Notice that the black queen and the black king have switched positions. However, this can happen only if some pawns have been moved. Therefore we can conclude that the bottom row on the diagram is actually the 8th row of the chessboard. All black and all white pieces have reached their respective opposite sides of the board.

Now White’s first move is Kb8-d7. The only moves black can play are with the knights. If Black plays Kb1-a3, Kb1-c3 or Kg1-h3, white mates in 2 more moves – Kd7-c5 and Kc5-d3. If Black moves Kg1-f3, then after Kd7-c5 Black can delay the mate by playing Kf3-e5. However, after the white queen takes it with Qxe5, Kc5-d3 is unavoidable.

Mate No Matter What

If White is to play, can he always mate Black in 2 moves, regardless of the moves played before?

The first thing to notice is that since the last move was made by Black, either the king or the rook was moved and therefore Black cannot castle anymore. Now White plays Qa1 and no matter what is Black’s next move, Qh8 gives check-mate.