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 languageEnglish
Title of host publicationFun with Algorithms - 6th International Conference, FUN 2012, Proceedings
Pages334-345
Number of pages12
DOIs
Publication statusPublished - 2012
Event6th International Conference on Fun with Algorithms, FUN 2012 - Venice, Italy
Duration: 2012 Jun 42012 Jun 6

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7288 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference6th International Conference on Fun with Algorithms, FUN 2012
CountryItaly
CityVenice
Period12/6/412/6/6

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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