Hitori number

Akira Suzuki, Kei Uchizawa, Takeaki Uno

研究成果: Conference contribution

1 被引用数 (Scopus)

抄録

Hitori is a popular "pencil-and-paper" puzzle game. In n-hitori, we are given an n ×n rectangular grid of which each square is labeled with a positive integer, and the goal is to paint a subset of the squares so that the following three rules hold: Rule 1) No row or column has a repeated unpainted label; Rule 2) Painted squares are never (horizontally or vertically) adjacent; Rule 3) The unpainted squares are all connected (via horizontal and vertical connections). The grid is called an instance of n-hitori if it has a unique solution. In this paper, we introduce hitori number defined as follows: For every integer n≥2, hitori number h(n) is the minimum number of different integers used in an instance where the minimum is taken over all the instances of n-hitori. We then prove that ⌈(2n-1)/3⌉ ≤ h(n)≤2⌈n/ 3⌉+1.

本文言語English
ホスト出版物のタイトルFun with Algorithms - 6th International Conference, FUN 2012, Proceedings
ページ334-345
ページ数12
DOI
出版ステータスPublished - 2012
イベント6th International Conference on Fun with Algorithms, FUN 2012 - Venice, Italy
継続期間: 2012 6 42012 6 6

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
7288 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Conference

Conference6th International Conference on Fun with Algorithms, FUN 2012
国/地域Italy
CityVenice
Period12/6/412/6/6

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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