September 26, 2026

Math Puzzle: What is the longest sequence of captures in checkers?

In American checkers rules, pieces only occupy the dark squares of an 8 x 8 checkerboard, and pieces can capture neighboring opposing pieces by jumping over them. A regular piece can capture an opposing piece when it is diagonally adjacent to that piece and the square directly beyond the to-be-captured piece is vacant. If capturing a different piece from this new square is legal, then the piece continues capturing until no further capture is available. Kings capture other pieces the same way but can also move backward, and kings can move forward and backward within the same turn. When tallying captured pieces, kings count the same as unpromoted checkers—each only contributes one piece to the count.

What is the maximum number of pieces that can be captured in a single turn of American checkers?

You can tinker with a digital checkerboard by clicking “Set up position” here.

The maximum number of checkers that can be captured in a single turn is nine.

Graphic shows a checkerboard with each row of squares labeled 1 through 8. A series of arrows represents a sequence of moves by the capturing piece. Starting in a dark square in the lower left corner, it jumps diagonally over nine other pieces in the following sequence: up and to the right, down and to the right, up and to the right, up and to the left, down and to the left, up and to the left, up and to the right, down and to the right, up and to the right. — Amanda Montañez

To see why you can’t exceed nine captures, number the rows as above and observe that checkers in odd-numbered rows can only capture checkers in even-numbered rows, and vice versa. Furthermore, if a capturing piece begins in an odd-numbered row, then it also ends its capture in an odd-numbered row (and captures that begin in even-numbered rows end in even-numbered rows). So the pieces captured on a single turn must all reside in odd rows or even rows. This cuts the 32 dark squares into only 16 possible slots for pieces captured on a single turn. Also, pieces on the very edge of the board can never be captured because no vacant square can lie beyond them. There are seven dark squares in odd-numbered rows on the edge of the board and seven in even-numbered rows. This lowers the 16 available squares from each parity down to nine.

Although nine sequential captures almost certainly would never occur in a real game, it is possible through legal (albeit bizarre) play. Here is a sample “proof game” that shows how it could happen.

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