What is the maximum number of black and white pieces which are relevant in a checkmate position (by White)? That is if any piece (black or white) was removed from the board, the checkmate would not be possible because that piece is relevant or has a role in such checkmate position because it may be: (1) checking the king (2) blocking a square where the checked king can move (3) attacking the unoccupied square where the checked king can move (4) preventing the king or other pieces to capture or block the checking piece. (Note that there shall be no idle or useless piece including the White king)
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2 Answers
Addendum 6/24/2023: It turns out that 20 pieces actually can be done in a manner that feels so obvious now. Removing wPf6 would cause an illegal position, and removing wBg7 would leave f6 unguarded.
[FEN "8/2B1R1B1/1N1rnP2/1Qq1knR1/2pP1r2/2K1bPB1/4R3/8 w - - 0 1"]
I found another, far funnier, reason why a piece can't be removed; the position would otherwise be illegal!
Using this idea, I've managed 19 pieces. White's pieces can't be taken, with the White king unmoveable, or else the checkmate is null. Black's pieces prevent illegality and "guard" c4, minus the e6 block.
[FEN "8/2B1R3/1N1rnp2/1Qq1knR1/2pP1r2/2K1bPB1/4R3/8 w - - 0 1"]
answered Mar 8, 2021 at 17:32
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@blademan9999 You are absolutely incorrect. It is needed for the wK to not be in check. Commented Feb 18 at 12:29
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@blademan9999 What are you on about? If the bPc4 is not there, the position is illegal from the bQ checking the wK. Commented Feb 28 at 0:46
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I hope I understood it right...
[FEN "1B2R2B/1Nq1b3/2P2n2/4kP2/2K2n2/4bP2/Qr5B/B3R3 w - - 0 1"]
Also 19, but more chances to improve it. (The problem is that the king should not be superfluous. If the question had been formulated as "#, -any piece, not #, maybe because illegal", I get 20.)
answered Mar 9, 2021 at 9:39
