A polyomino puzzle for arithmetic practice

Article type: Research Article

Authors: Foxcroft, Jeremy^{a; *} | Ashlock, Daniel^b

Affiliations: [a] School of Computer Science, University of Guelph, Canada. E-mail: jfoxcrof@uoguelph.ca | [b] Department of Mathematics & Statistics, University of Guelph, Canada

Correspondence: [*] Corresponding author. E-mail: jfoxcrof@uoguelph.ca.

Abstract: Recent trends in mathematics education emphasize discovery learning over drill. This has proven to be a bad idea in some cases, for the simple reason that practice is required to learn basic arithmetic skills. Drills in arithmetic skills can be made interesting through gamification. This study proposes a family of puzzles that gamify arithmetic practice. The puzzles are designed with an evolutionary algorithm forming an instance of automatic content generation. Two methods of evolutionary puzzle design are presented and discussed. The first method used transformed the problem into an almost trivial optimization. The second algorithm was designed to avoid the flaws of the first and produced a huge variety of puzzles. A hardness measure, based on the difficulty experienced by the evolutionary puzzle generator, is employed. The hardness measure is tested on a large collection of puzzles produced with the evolutionary automatic content generation system. An initial assumption, that all the pieces in the puzzle must be used to achieve a maximum score, was shown to be incorrect in puzzles located via automatic search. Two classes of puzzle are defined: those where the optimal solution uses all pieces and those where the optimal solution fails to use at least one piece. The latter sort of puzzle were found to be far more common in the search space.

Keywords: Procedural content generation, gamification, evolutionary computation, puzzles

DOI: 10.3233/ICG-200170

Journal: ICGA Journal, vol. 42, no. 4, pp. 272-286, 2020