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I am looking for a position in which all possible moves are checkmate. This means, that if the player does not want to checkmate the opponent, because for example he feels sorry for him, even in that case he is forced to checkmate him. He cannot avoid it. Can you tell me an example? White or black does not matter.
Also, I feel this can be done only if there is a very small number of possible moves. For example 1 or 2.
I just remembered a class of chess problem; see item 267 of Tim Krabbé's Open Chess Diary (his whole site is highly recommended):
[Title "White mates in 7, Noam Elkies, 2004."]
[FEN "KBk5/P1P4p/2Pp3P/P6p/2p3rP/2P3pB/6P1/8 w KQkq - 0 1"]
Spoiler: White has some choices here, he can choose different move orders. But it's always checkmate on move 7, no matter what.
The current record for most forced checkmates in a legal position with no promoted pieces is 29:
[Title "Harold Holgate Cross, The Problemist FCS Apr 1936, 2251"]
[StartFlipped "0"]
[fen "8/1b6/p1N5/P1r5/P3KPr1/QBk1NRP1/P2R1P2/4B3 w KQkq - 0 1"]
PDB has it at id P1178654. White is to move.
(For the record where the position must be legal and may have promoted pieces, see Rewan Demontay's answer.)
One source is Dickins & Ebert, "100 Classics of the Chessboard", no.94b
I found two cases of 55 forced mates with promoted pieces in Tim Krabbe’s Diary Entry #383.
[Title "Ludwig Zagler, Feenschach 1972, 55 Forced Mates In 1"]
[FEN "1rB1Q1Q1/1PRQ3Q/2b2k2/2pQ1N1Q/4KRPp/5N2/1R6/B3nn1b w - - 0 1"]
[Title "Sampsa Lahtonen, Tim Krabbe's Website Diary Entry #383 2008, 55 Forced Mates In 1"]
[FEN "B3n1bb/1R6/4pN2/4KRPp/2pQ1N1Q/2b2k2/1PRQ3Q/1rB1Q1Q1 w - - 0 1"]
@Rosie F’s answer contains the record without promoted piece,
