Shikaku
Logic puzzle
title: "Shikaku" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["logic-puzzles", "rectangular-subdivisions", "np-complete-problems", "japanese-board-games"] description: "Logic puzzle" topic_path: "philosophy" source: "https://en.wikipedia.org/wiki/Shikaku" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0
::summary Logic puzzle ::
|direction=vertical |image1=shikaku start.png |caption1=An initial configuration. |image2=shikaku end.png |caption2=A solution. Shikaku is a logic puzzle published by Nikoli.
History
The game was invented by Yoshinao Anpuku, a math student at the University of Kyoto, in 1989 and published by Japanese games magazine Nikoli under the name "Shikaku". The puzzle later spread to other publications and has been adapted into video games.
Rules
Shikaku is played on a rectangular grid. Some of the squares in the grid are numbered. The objective is to divide the grid into rectangular and square pieces such that each piece contains exactly one number, and that number represents the area of the rectangle.{{cite journal | last = Wanko | first = Jeffrey J. | date = November 2009 | doi = 10.5951/mt.103.4.0266 | issue = 4 | journal = The Mathematics Teacher | jstor = 20876604 | pages = 266–271 | publisher = National Council of Teachers of Mathematics | title = Japanese logic puzzles and proof | volume = 103}}
Computational complexity
Determining whether a given instance of Shikaku has a valid solution has been proven to be NP-complete.{{cite journal | last1 = Takenaga | first1 = Yasuhiko | last2 = Aoyagi | first2 = Shintaro | last3 = Iwata | first3 = Shigeki | last4 = Kasai | first4 = Takumi | journal = Congressus Numerantium | mr = 3220078 | pages = 119–127 | title = Shikaku and ripple effect are NP-complete | volume = 216 | year = 2013}}
References
References
- (20 September 2021). "Shikaku (Divide by Box)". Nikoli.
- Milner, Susan. "Mathematical Logic Puzzles on a Grid". Canadian Mathematical Society.
- Bellos, Alex. (May 23, 2022). "Inside Japan's Cult-Favorite Puzzle Laboratory". [[Atlas Obscura]].
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