7

What is the highest number of pieces from one side that can be involved in a checkmate? "Involved in a checkmate" is defined below.

A non-king piece is involved in a checkmate 'if removing it from the checkmate position would change the position to one which is either not checkmate or is illegal'. The king is involved in a checkmate if it is the only piece of the checkmating side that attacks one of the other king's escape squares.

Rewan Demontay
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    Does it count as an "illegal" position if the position itself doesn't violate the rules, but there is no possible way to get there in a legal game? – D M Nov 21 '17 at 01:24
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    Yes indeed, any position which can't be reached in a legal game is illegal. –  Nov 21 '17 at 01:35

4 Answers4

16

Here is a solution with all 16 white pieces, all mandatory for checkmate, without promoted units and without needing to protect the white king from checks. If you remove any white piece but the king, the position is still legal but not a checkmate anymore. Moving the wK to a random square (say, h1) would also destroy the mate.

QNr1R1b1/P1BpnP2/3P4/qP4Pr/Rn2kP2/1N4PB/2P2K2/8 w - - 0 1

Last move is Nc6-b8# or d5-d6#.

Evargalo
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9

My original thought was that the limit was nine pieces; one for each of the 8 squares around the king, plus one for the mating check on the king's square.

[FEN "8/2K5/8/3Pk3/2P2PPB/3P2P1/2N5/8 b - - 0 1"]
[startflipped ""]

But, as someone pointed out in a comment, pieces can become "necessary" even if they aren't controlling one of those squares. If the Black pieces don't have to be "necessary", then we can have a board where all White pieces are "necessary" for below to be a legal checkmate position.

Although, seven of them are just preventing check. The rest do the actual job of checkmate.

[FEN "3b1q1q/1N2PRQ1/rR3KBr/B4PP1/2Pk1r1b/1P2P1N1/2P2P2/8 b - - 0 1"]
[startflipped ""]
Rewan Demontay
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D M
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    If black pieces are allowed, this is not the limit! You could have a situation where the check-mating piece needs to be protected from capture by blocking pieces. For instance in your example you could place a black rook on f1 and say a white pawn on f2. Without the pawn on f2 it would not be checkmate, because black had Rxf4. – user1583209 Nov 21 '17 at 00:35
  • @user1583209 Hmm, good point... – D M Nov 21 '17 at 01:05
  • As mentioned above, pieces could be required to block pieces from capturing the checkmating piece. They could also be required to block a piece from blocking. Another idea is to have a piece which pins an enemy piece which could block or capture the checkmating piece. You could also have a discovered check by a piece, for example a bishop in the corner, where the piece moving out of the way is needed because the position would be illegal without it. –  Nov 21 '17 at 04:22
  • Here is an example where removing a piece would make the position illegal due to castling rules: [FEN "7R/8/8/7b/8/5P2/3R4/2KR3k w - - 0 1"] –  Nov 21 '17 at 05:09
  • Here is another example involving en passant in which the pawn on d6 is needed to make the position legal. The last move in the game involved removing a blocker which was in the checkmating piece's line of attack:[FEN "8/R7/3Pk3/6K1/5P2/B3N3/B3R3/1N6 w - - 0 1"]. –  Nov 22 '17 at 00:12
  • Interestingly, in the example [FEN "8/R7/3Pk3/6K1/5P2/B3N3/B3R3/1N6 w - - 0 1"], removing the b1 knight after removing the d6 pawn makes the position a legal checkmate again. In the following en passant example, removing any piece or pieces messes up the checkmate or is an illegal position: [FEN "8/4K3/2kP4/8/N1Q5/8/6B1/8 b - -"] –  Nov 22 '17 at 01:16
1

Here's another way to involve all 16 White units. This time the check is orthogonal.

[Title "All 16 White units in the mating-net"]
[fen "r2N1R2/1p2pn2/PBB1P3/Q4kPP/8/5nPK/PNPP1R2/q1r1b3 w - - 0 1"]
[StartFlipped "0"]

    

  1.

wNd8 stops Ke6; wPg5, Kf6; wPh5, Kg6; wBc6, Ke4; wPg3, Kf4; wK, Kg4; wRf8, N7e5; wPa6, Rxa5; wBb6, b5; wPe6, e5; wPa2, Qxa5; wNb2, Qe5; wPc2, Rc5; wPd2, Bxa5; wRf2, N3e5.

Legality: Perhaps wPa6 did bxPa and wPg5 did fxPg. (Or perhaps one of them captured [bBc8].)

Rosie F
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0

Here is another 16-piece set, in which I strived for economy. I chipped down to 5 Black pieces; three less than @Evargalo, for whom I must thank for their matrix. I've also incorporated a new reason for needing a piece.

[FEN "QB1rR3/P1NPnN2/1P6/1rP5/4k3/1PP3PB/qRKP4/8 w - - 0 1"]

Here is a list regarding why each piece is needed.

  • wKc2: Guards d3.
  • wQa8: No checkmate.
  • wRb2: Without it, the position is illegal.
  • wRe8: Pins bNe7.
  • wBb8: Prevents bRxa8.
  • wBh3: Guards f6.
  • wNc7: Without it, the wQ's check is impossible, and thus the position is illegal. It is impossible for c6xd7+ to have been the last move, as that would require one too many captures.
  • wNf7: Guards e5.
  • wPa7: Prevents bQxa8.
  • wPb3: Prevents bQd5.
  • wPb6: Prevents bRb7.
  • wPc3: Guards d4.
  • wPc5: Prevents bRd5.
  • wPd2: Guards e3.
  • wPe7: Prevents bRd5.
  • wPf3: Guards f4.
Rewan Demontay
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