Solving Scramble Squares puzzles with repetitions

Callahan, Jason; Mota, Maria

doi:10.2140/involve.2019.12.343

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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

Abstract

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

Keywords

graph theory, directed graphs

Mathematical Subject Classification 2010

Primary: 05C75, 94C15

Milestones

Received: 20 December 2017

Revised: 20 March 2018

Accepted: 4 April 2018

Published: 8 October 2018

Communicated by Kenneth S. Berenhaut

Authors

Jason Callahan
Department of Mathematics St. Edward’s University Austin, TX United States

Maria Mota
St. Edward’s University Austin, TX United States

Vol. 12, No. 2, 2019