A puzzle involving checkerboards: grids of squares alternating black and white in color, most commonly an 8x8 board.

A checkerboard is a grid of squares with alternating black and white colors, most commonly an 8x8 board but not necessarily even rectangular.

Many checkerboard puzzles concern the adjacency relations between squares:

  • Two squares are said to be horizontally or vertically adjacent (sometimes also called orthogonally adjacent or strongly adjacent), if they share a common edge. Every corner/boundary/interior square has 2/3/4 horizontally or vertically adjacent neighbors.

  • Two squares are said to be weakly adjacent (sometimes also called King-adjacent), if they share a common edge or a common point. Every square has at most eight weakly adjacent neighbors.

Example: The mutilated chessboard problem considers a standard 8x8 chessboard that has two diagonally opposite corners removed (hence leaving 62 squares). Is it possible to place 31 dominoes of size 2x1 so as to cover all of these squares?

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