On the Difficulty of Nonograms

Article type: Research Article

Authors: Batenburg, K. Joost^{a; 1} | Kosters, Walter A.^{b; 2}

Affiliations: [a] Centrum Wiskunde & Informatica, Amsterdam, The Netherlands; Mathematical Insitute, Leiden University, Leiden, The Netherlands; Vision Lab, University of Antwerp, Wilrijk, Belgium | [b] Leiden Institute of Advanced Computer Science, Leiden University, The Netherlands

Note: [1] email: [email protected]

Note: [2] email: [email protected]

Abstract: Nonograms are a popular type of logic puzzles, where a pixel grid has to be filled with black and white pixels, based on a description that indicates the lengths of the consecutive black segments for each row and column. While the Nonograms that can be found in puzzle books can typically be solved by applying a series of highly local reasoning steps regarding single rows and columns, the general Nonogram problem is NP-hard. In this article, we explore the difficulty distributions for puzzles between these two extremes. After defining several difficulty measures and subclasses, we analyze the frequencies of various types of puzzles within the set of all possible Nonograms, using both exhaustive enumeration and sampling.

DOI: 10.3233/ICG-2012-35402

Journal: ICGA Journal, vol. 35, no. 4, pp. 195-205, 2012