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.

2
  • 1
    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, 2017 at 1:24
  • 3
    Yes indeed, any position which can't be reached in a legal game is illegal.
    – user11382
    Nov 21, 2017 at 1:35

4 Answers 4

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 ""]
6
  • 7
    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. Nov 21, 2017 at 0:35
  • @user1583209 Hmm, good point...
    – D M
    Nov 21, 2017 at 1:05
  • 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.
    – user11382
    Nov 21, 2017 at 4:22
  • 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"]
    – user11382
    Nov 21, 2017 at 5:09
  • 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"].
    – user11382
    Nov 22, 2017 at 0:12
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#.

0
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].)

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.
1
  • Maybe a further task could be to have all the wP on their original files...
    – Evargalo
    Jun 26, 2023 at 7:30

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