Geometric Chess Puzzles

These puzzles will test your knowledge of chess and math. Detailed answers are available at Geometric Chess Puzzle Solutions.

Start with a chess board and a large supply of chess pieces.

• In each puzzle you have a standard chessboard with algebraic coordinates, and 64 chess pieces of the same type.
• You need to place as many pieces as possible on the chessboard, so that no piece can capture another piece on the next move.
• You can place pieces on any squares you choose, but no more than one piece can be placed on each square.
• All puzzles have more than one solution.
• Two solutions are considered to be the same if they have the same pieces on the same squares, and each square is labeled with algebraic coordinates.
• After determining the maximum number of pieces that can be placed on the board in each puzzle, specify the number of different solutions which allow you to place that number of pieces on the board.
• Insert a chess diagram for each puzzle displaying one position which solves that puzzle.

In puzzles 1 to 4, there are 32 white pieces and 32 black pieces. These pieces move like standard chess pieces, and pieces of different colors can capture each other, but pieces of the same color cannot capture each other.

Puzzle 1) You have 32 white knights and 32 black knights. The number of white knights on the board must equal the number of black knights on the board. What is the maximum number of knights that can be placed on the board, so that no knight can capture another knight?

Puzzle 2) You have 32 white bishops and 32 black bishops. The number of white bishops on the board must equal the number of black bishops on the board. What is the maximum number of bishops that can be placed on the board, so that no bishop can capture another bishop?

Puzzle 3) You have 32 white rooks and 32 black rooks. The number of white rooks on the board must equal the number of black rooks on the board. What is the maximum number of rooks that can be placed on the board, so that no rook can capture another rook?

Puzzle 4) You have 32 white queens and 32 black queens. The number of white queens on the board must equal the number of black queens on the board. What is the maximum number of queens that can be placed on the board, so that no queen can capture another queen?

In puzzles 5 to 8, all the pieces are white. These pieces move like standard chess pieces, except that white pieces can capture other white pieces.

Puzzle 5) You have 64 white knights. What is the maximum number of knights that can be placed on the board, so that no knight can capture another knight?

Puzzle 6) You have 64 white bishops. What is the maximum number of bishops that can be placed on the board, so that no bishop can capture another bishop?

Puzzle 7) You have 64 white rooks. What is the maximum number of rooks that can be placed on the board, so that no rook can capture another rook?

Puzzle 8) You have 64 white queens. What is the maximum number of queens that can be placed on the board, so that no queen can capture another queen?