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Solving scramble squares puzzles with repetitions. (English) Zbl 1402.05203

Summary: 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.

MSC:

05C90 Applications of graph theory
91A99 Game theory
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References:

[1] ; de Carteblanche, Eureka, 9, 9 (1947)
[2] 10.2307/2688218 · Zbl 0217.02203 · doi:10.2307/2688218
[3] 10.2140/involve.2012.5.313 · Zbl 1264.05136 · doi:10.2140/involve.2012.5.313
[4] 10.1007/BFb0060130 · doi:10.1007/BFb0060130
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