The fewest clues problem of picross 3D

Kei Kimura, Takuya Kamehashi, Toshihiro Fujito

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)


Picross 3D is a popular single-player puzzle video game for the Nintendo DS. It is a 3D variant of Nonogram, which is a popular pencil-and-paper puzzle. While Nonogram provides a rectangular grid of squares that must be filled in to create a picture, Picross 3D presents a rectangular parallelepiped (i.e., rectangular box) made of unit cubes, some of which must be removed to construct an image in three dimensions. Each row or column has at most one integer on it, and the integer indicates how many cubes in the corresponding 1D slice remain when the image is complete. It is shown by Kusano et al. that Picross 3D is NP-complete. We in this paper show that the fewest clues problem of Picross 3D is ΣP 2 -complete and that the counting version and the another solution problem of Picross 3D are #P-complete and NP-complete, respectively.

Original languageEnglish
Title of host publication9th International Conference on Fun with Algorithms, FUN 2018
EditorsGiuseppe Prencipe, Hiro Ito, Stefano Leonardi, Linda Pagli
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Number of pages2263
ISBN (Electronic)9783959770675
Publication statusPublished - Jun 1 2018
Externally publishedYes
Event9th International Conference on Fun with Algorithms, FUN 2018 - La Maddalena Island, Italy
Duration: Jun 13 2018Jun 15 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference9th International Conference on Fun with Algorithms, FUN 2018
CityLa Maddalena Island

All Science Journal Classification (ASJC) codes

  • Software


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