I am running a small chess school for beginners. During a class I asked a child to compose a checkmate position using only king, bishop and knight against the opposing king in a corner. Then I made the task tougher by placing the opposing king in the middle edge. And finally I asked him on purpose to try the same in the center of the board, to see if he was able to conclude that the task was impossible. Not only he did, but he also proposed to try the task in the center of the board with a third minor piece. To my surprise, this task seems to be impossible as well. We tried with any combination of three minor pieces plus the king. Is it true that this task is not possible?
asked Oct 22, 2021 at 15:33
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Are you asking about three specific minor pieces, or any three?– Robbie GoodwinOct 25, 2021 at 19:16
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@RobbieGoodwin Any three, as per the title. Could be three of the same kind. The given answer covers this case.– Daniel Alfredo SottileOct 26, 2021 at 16:55
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How does "three of the same kind" work, except for pawns?– Robbie GoodwinOct 31, 2021 at 23:27
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@RobbieGoodwin The possible combinations are: 2 knight and a bishop, 2 knights and the opposite coloured bishop, or 2 bishops and a knight, or three knights, or three bishops. Pawns are not considered minor pieces -> en.wikipedia.org/wiki/Glossary_of_chess– Daniel Alfredo SottileNov 1, 2021 at 17:38
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1Thanks and sorry I was silly enough to assume you were working only with the starting pieces!– Robbie GoodwinNov 5, 2021 at 13:11
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1 Answer
It is indeed impossible to construct a mating net with king + 3 minor pieces against a lone king in the center of the board.
A mating net would require that all 9 squares in the 3x3 block which contains the opposing king be under attack. The king can only cover 3 of those 9 squares since it can't be next to the opposing king. This would leave a 3x2 rectangle of squares which would need to be covered by the 3 minor pieces. That rectangle has 3 black and 3 white squares. Any minor piece can cover 2 of those 6 squares -- but those squares would need to be of the same color. (One might quibble that a bishop which is directly adjacent to the opposing king could cover 3 squares, but that would be capturable by the king unless supported by another piece, the net result being just 3 squares covered by 2 pieces). If 1 of the minor pieces covers 2 of the white squares and 1 covers 2 of the black squares, the remaining piece would have to cover 1 white and 1 black square, but that is impossible.
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Hey, how did you do this? Did you actually think this through in your head or did you sit with a chess board and tried it out? I can't even think about this whole thing by reading your answer. I can only imagine how good you are. Oct 24, 2021 at 21:19
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2Might be worth noting that you can stalemate a king on (say) d5 with a nicely symmetrical arrangement of king at d7, bishops at b6 and f6 and knight at d2. But you can't attack him as well... (p.s. both your bishops are same colour, so you must've promoted one of them). Oct 25, 2021 at 9:21
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1@OscarBravo You could replace one of the bishops with a knight covering the same to squares next to the king for a slightly less artificial position. Oct 25, 2021 at 17:17
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1@OscarBravo Another configuration could be done with 3 knights, 2 on the same file as the enemy king 2 and 3 spaces away, and a a 3rd knight on the other side of the king and one file over (diagonally adjacent to it). Your king would be on the same file as the enemy king and 2 knights protecting the 3rd knight and guarding the other 2 spaces on that row. Or the 3rd knight could be on the same row as the enemy king 2 files away. Oct 25, 2021 at 17:59