3

What is the most number of pieces from one side that can be involved in a checkmate if we define 'involved in a checkmate' as follows?

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.

  • 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 '17 at 1:24
  • 3
    Yes indeed, any position which can't be reached in a legal game is illegal. – user11382 Nov 21 '17 at 1:35
5

My original thought was that the limit was nine pieces; one for each of the 8 squares the king can run to, plus one for check:

8/2K5/8/3Pk3/2P2PPB/3P2P1/2N5/8 w - - 0 1

But as someone mentioned 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 the white pieces are "necessary" to make this be a legal checkmate, although seven of them are just preventing a check. The rest do the actual job of checkmate.

3b1q1q/1N2PRQ1/rR3KBr/B4PP1/2Pk1r1b/1P2P1N1/2P2P2/8 b - - 0 1
  • 3
    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 0:35
  • @user1583209 Hmm, good point... – D M Nov 21 '17 at 1:05
  • Nice solution!! – user11382 Nov 21 '17 at 3:06
  • 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 '17 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 '17 at 5:09
9

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#.

  • 2
    Another nice 16-piece checkmate. :) – user11382 Nov 22 '17 at 3:57
  • And it vastly minimizes the number of black pieces needed to as well, quite nicely! No promoted pieces are even needed here! – Rewan Demontay May 15 at 12:58

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