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Computational Complexity and an Integer Programming Model of Shakashaka
Erik D. DEMAINE Yoshio OKAMOTO Ryuhei UEHARA Yushi UNO
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2014/06/01
Online ISSN: 1745-1337
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
integer programming, NP-completeness, pencil-and-paper puzzle, Shakashaka,
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Shakashaka is a pencil-and-paper puzzle proposed by Guten and popularized by the Japanese publisher Nikoli (like Sudoku). We determine the computational complexity by proving that Shakashaka is NP-complete, and furthermore that counting the number of solutions is #P-complete. Next we formulate Shakashaka as an integer-programming (IP) problem, and show that an IP solver can solve every instance from Nikoli's website within a second.