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.
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References
Hearn, R.A., Demaine, E.D.: Games, Puzzles, and Computation, pp. 112–115. A.K. Peters, CRC Press (2009)
Gander, M., Hofer, C.: Hitori Solver: Extensions and Generation. Bachelor Thesis, University of Innsbruck (2007)
Suzuki, A., Uchizawa, K., Uno, T.: Manuscript
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© 2012 Springer-Verlag Berlin Heidelberg
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Suzuki, A., Uchizawa, K., Uno, T. (2012). Hitori Number. In: Kranakis, E., Krizanc, D., Luccio, F. (eds) Fun with Algorithms. FUN 2012. Lecture Notes in Computer Science, vol 7288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30347-0_33
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DOI: https://doi.org/10.1007/978-3-642-30347-0_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30346-3
Online ISBN: 978-3-642-30347-0
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