A graph-theoretical approach to solving Scramble Squares puzzles

Abstract

A Scramble Squares puzzle is made up of nine square pieces such that each edge of each piece contains half of an image. A solution to the puzzle is obtained when the pieces are arranged in a $3\times 3$ grid so that the adjacent edges of different pieces together make up a complete image. We describe a graph-theoretical approach to solving Scramble Squares puzzles and a method for decreasing randomness in the backtracking solution algorithm.