Vol. 5, No. 3, 2012

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A graph-theoretical approach to solving Scramble Squares puzzles

Sarah Mason and Mali Zhang

Vol. 5 (2012), No. 3, 313–325
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 × 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.

Keywords
graph theory, algorithms
Mathematical Subject Classification 2010
Primary: 05C75, 94C15
Milestones
Received: 23 August 2011
Revised: 15 December 2011
Accepted: 15 December 2011
Published: 14 April 2013

Communicated by Arthur T. Benjamin
Authors
Sarah Mason
Department of Mathematics
Wake Forest University
127 Manchester Hall
Winston-Salem, NC 27109
United States
Mali Zhang
Davidson College
Davidson, NC 28035
United States