shikaku
{{Short description|Logic puzzle}}
{{Multiple image
|direction=vertical
|image1=shikaku start.png
|caption1=An initial configuration.
|image2=shikaku end.png
|caption2=A solution.
}}
{{nihongo|Shikaku|四角に切れ|Shikaku ni Kire|also anglicised as Divide by Box{{cite web|title=Shikaku (Divide by Box)|date=20 September 2021 |publisher=Nikoli|url=https://www.nikoli.co.jp/en/puzzles/shikaku/|access-date=2024-05-21}} or Rectangles{{cite book|title=Mathematical Logic Puzzles on a Grid|contribution=Chapter 1: Rectangles|pages=1–7|series=A Taste Of Mathematics / Aime-T-On Les Mathématiques|volume=17|publisher=Canadian Mathematical Society|first=Susan|last=Milner|author-link= Susan Milner |url=https://cms.math.ca/wp-content/uploads/2022/10/ATOM-XVII-Mathematical-Logic-Puzzles-on-a-Grid-1.pdf|isbn=978-0-919558-30-4}}}} is a logic puzzle published by Nikoli.
History
The game was invented by Yoshiano 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.{{cite web |last=Bellos |first=Alex |date=May 23, 2022 |title=Inside Japan's Cult-Favorite Puzzle Laboratory |url=https://www.atlasobscura.com/articles/nikoli-puzzle-communication |work=Atlas Obscura |accessdate=May 14, 2024}}
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}}