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?
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Are you asking about three specific minor pieces, or any three? – Robbie Goodwin Oct 25 '21 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 Sottile Oct 26 '21 at 16:55
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How does "three of the same kind" work, except for pawns? – Robbie Goodwin Oct 31 '21 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 -> https://en.wikipedia.org/wiki/Glossary_of_chess – Daniel Alfredo Sottile Nov 01 '21 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 Goodwin Nov 05 '21 at 13:11
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Oh ok @RobbieGoodwin, in fact what you said could be a nice challenge! – Daniel Alfredo Sottile Nov 05 '21 at 13:21
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Thanks and in fact, I think John Coleman's 3x3 net works - or rather, can't be made to -and covering even the 8 places round the king would need 5 bishops or 4 knights. – Robbie Goodwin Nov 05 '21 at 13:36
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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.
John Coleman
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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. – RoundHouse Oct 24 '21 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). – Oscar Bravo Oct 25 '21 at 09:21
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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. – Troy Daniels Oct 25 '21 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. – Darrel Hoffman Oct 25 '21 at 17:59
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@John Coleman How is it your king can only cover 3 of those 9 squares? – Robbie Goodwin Oct 26 '21 at 20:00