# Hitori number

Akira Suzuki, Kei Uchizawa, Takeaki Uno

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 Fun with Algorithms - 6th International Conference, FUN 2012, Proceedings 334-345 12 https://doi.org/10.1007/978-3-642-30347-0_33 Published - 2012 6th International Conference on Fun with Algorithms, FUN 2012 - Venice, Italy継続期間: 2012 6 4 → 2012 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 0302-9743 1611-3349

### Conference

Conference 6th International Conference on Fun with Algorithms, FUN 2012 Italy Venice 12/6/4 → 12/6/6

## 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）

## フィンガープリント

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