Vol. 12, No. 2, 2019

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Solving Scramble Squares puzzles with repetitions

Jason Callahan and Maria Mota

Vol. 12 (2019), No. 2, 343–349
DOI: 10.2140/involve.2019.12.343

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 3 × 3 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 2 × 2 Scramble Squares puzzles. We use a similar approach to establish necessary and sufficient conditions for solutions with repetitions to 2 × 2 Scramble Squares puzzles.

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graph theory, directed graphs
Mathematical Subject Classification 2010
Primary: 05C75, 94C15
Received: 20 December 2017
Revised: 20 March 2018
Accepted: 4 April 2018
Published: 8 October 2018

Communicated by Kenneth S. Berenhaut
Jason Callahan
Department of Mathematics
St. Edward’s University
Austin, TX
United States
Maria Mota
St. Edward’s University
Austin, TX
United States