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Can you place the eight (non-pawn) pieces of one color on an otherwise empty chess board, such that every square (including the squares that pieces are on), is attacked / defended?

This is a problem that I wrestled with in high school and I'm not sure I've seen it discussed anywhere else.

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  • If a piece is on a square, does that square count as being attacked? Or does another, separate piece, have to be attacking it?
    – odinchess.com
    Commented Dec 6, 2021 at 23:22
  • 11
    He's just asking if theoretically you can place the 8 pieces on the board to attack each square. Not a real chess game.
    – odinchess.com
    Commented Dec 6, 2021 at 23:49
  • 4
    This might be better suited to puzzling.stackexchange.com than to chess.
    – Guntram Blohm
    Commented Dec 7, 2021 at 8:23
  • 3
    This would be trivial with eight queens or eight rooks, no?
    – Hearth
    Commented Dec 7, 2021 at 16:09
  • 2
    To be clear, you can use 8 queens if you wanted? Or is it just with the starting pieces (sans pawns)?
    – BruceWayne
    Commented Dec 7, 2021 at 18:57

1 Answer 1

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If the two bishops travel on the same color squares, then all 64 squares can be covered by the eight pieces. However, if the bishops must travel on opposite colors, then the maximum number of squares that can be covered is 63. See Eight Pieces Cannot Cover a Chess Board for a complete discussion.

Here is one of several possible 63 square solutions for opposite-color bishops:

[fen "8/3nb2r/3n4/8/r7/1b6/2q2k2/8 w - - 1 1"]

The d7 knight is not under attack.

Here is one of the three solutions to covering all squares with same-color bishops:

[fen "r7/8/2b2k2/3n4/4n3/2q2b2/8/7r w - - 1 1"]

Citation:

Robison, Arch D., Brian J. Hafner, and S. S. Skiena. "Computer Games: Eight Pieces Cannot Cover a Chess Board." The Computer Journal 32, no. 6 (1989): 567-570.

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  • 7
    In the same-color bishop solution, I like how the queen isn't any more useful than the king in providing coverage.
    – Engineer Toast
    Commented Dec 7, 2021 at 14:11
  • 6
    @EngineerToast Almost. The queen covers the bishops and the king, the king doesn't.
    – Jens
    Commented Dec 7, 2021 at 14:26
  • 1
    @Jens Ah! Of course. I completely neglected coverage of the occupied squares.
    – Engineer Toast
    Commented Dec 7, 2021 at 14:27
  • 3
    The king is also covered by the knights, so that doesn't count. But yes, the queen is the only piece covering the bishops.
    – Deduplicator
    Commented Dec 7, 2021 at 17:30

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