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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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    This is NOT a duplicate. This question asks for both sides, while only one side is asked here: chess.stackexchange.com/questions/19207/… – Rewan Demontay Mar 8 at 17:11
  • Your stated requirement is only that a single piece cannot be removed without losing the mate (or legality). How about removing multiple units simultaneously? And do you agree with Rewan's idea illegality is another reason why a piece can't be removed? – Laska Mar 9 at 0:34
  • ..a piece that prevent kings in check is also relevant for legality but not stated in OP. Rewan Demontay's 18 pieces earlier solution has some pieces preventing White king in check but they also block the king's escape. – TSLF Mar 9 at 17:34
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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"]
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  • Depends: bQe3 instead of bBe3, +bPd3. Of course this means a promoted Q, but you never said that's forbidden ;-) Of course the position is illegal now, but this can easily be repaired with another promoted checking piece, say wBb2, and a bit of rearrangement. And I have some vague other ideas... – Hauke Reddmann Mar 8 at 21:43
  • @HaukeReddmann The point is that the pinned piece would capture the mating c4 pawn if not pinned. So another checking piece wouldn't do anything. – Rewan Demontay Mar 8 at 22:47
  • Pawn from d3 of course. – TSLF Mar 9 at 6:02
  • Ah, silly me, you do have promoted material. Need new glasses :-) Without promo, I manage 17. – Hauke Reddmann Mar 9 at 9:43
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I hope I understood it right...

[FEN "1B2R2B/1Nq1b3/2p2n2/Q3kP2/2K2n2/4bP2/1r5B/B3R3 w KQkq - 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.)

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  • Well done Hauke! – Rewan Demontay Mar 9 at 13:15
  • removal of Ba1 still is a checkmate but not removal of rb2 – TSLF Mar 9 at 17:18
  • @TSLF Are you blind??? Removing Ba1 allows Black to play 1... Rb5 and block the checkmate! – Rewan Demontay Mar 9 at 21:00
  • @RewanDemontay: Chess blindness (amaurosis scachistica tarraschii) happens to the best, e.g. I triumphed to have a position...uh-oh, I haven't, it's legal due to a double check. Back to the good old drawing board...BTW, despite much trying I could not improve 19, trying a bishop or knight check is even worse since you must maximize "far" pins (piece not adjacent to king). – Hauke Reddmann Mar 10 at 10:47

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