A Scramble Squares puzzle consists of nine square pieces with half of an image on each side. To solve the puzzle the pieces are arranged in a grid so that sides of adjacent pieces form complete images. A repetition is a half-image that appears more than once on a piece. Previous research uses a graph-theoretical approach to establish necessary and sufficient conditions for solutions without repetitions to Scramble Squares puzzles. We use a similar approach to establish necessary and sufficient conditions for solutions with repetitions to Scramble Squares puzzles.
"Solving Scramble Squares puzzles with repetitions." Involve 12 (2) 343 - 349, 2019. https://doi.org/10.2140/involve.2019.12.343