# Hitori number

Akira Suzuki, Kei Uchizawa, Takeaki Uno

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

1 Citation (Scopus)

## Abstract

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.

Original language 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, ItalyDuration: 2012 Jun 4 → 2012 Jun 6

### Publication series

Name 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

• Theoretical Computer Science
• Computer Science(all)

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