Sankaku-tori: An old Western-japanese game played on a point set

Takashi Horiyama, Takashi Iizuka, Masashi Kiyomi, Yoshio Okamoto, Ryuhei Uehara, Takeaki Uno, Yushi Uno, Yukiko Yamauchi

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We study a combinatorial game named '‘sankaku-tori’' in Japanese, which means '‘triangle-taking’' in English. It is an old pencil-and-paper game for two players played in Western Japan. The game is played on points on the plane in general position. In each turn, a player adds a line segment to join two points, and the game ends when a triangulation of the point set is completed. The player who completes more triangles than the other wins. In this paper, we formalize this game and investigate three restricted variants of this game. We first investigate a solitaire variant; for a given set of points and line segments with two integers t and k, the problem asks if you can obtain t triangles after k moves. We show that this variant is NP-complete in general. The second variant is the standard two player version, but the points are in convex position. In this case, the first player has a nontrivial winning strategy. The last variant is a natural extension of the second one; we have the points in convex position but one point inside. Then, it turns out that the first player has no winning strategy.

Original languageEnglish
Pages (from-to)708-715
Number of pages8
JournalJournal of information processing
Publication statusPublished - Aug 2017

All Science Journal Classification (ASJC) codes

  • General Computer Science


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