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Abstract
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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.
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Keywords
graph theory, directed graphs
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Mathematical Subject Classification 2010
Primary: 05C75, 94C15
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Milestones
Received: 20 December 2017
Revised: 20 March 2018
Accepted: 4 April 2018
Published: 8 October 2018
Communicated by Kenneth S. Berenhaut
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