Abstract
We discuss some new geometric puzzles and the complexity of their extension to arbitrary sizes. For gate puzzles and two-layer puzzles we prove NP-completeness of solving them. Not only the solution of puzzles leads to interesting questions, but also puzzle design gives rise to interesting theoretical questions. This leads to the search for instances of partition that use only integers and are uniquely solvable. We show that instances of polynomial size exist with this property. This result also holds for partition into k subsets with the same sum: We construct instances of n integers with subset sum O(n k+1), for fixed k.
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Part of this research was done when the first author was visiting Utrecht University, and during the Dagstuhl Seminar No. 06481 on Geometric Networks and Metric Space Embeddings in 2006.
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Alt, H., Bodlaender, H., van Kreveld, M. et al. Wooden Geometric Puzzles: Design and Hardness Proofs. Theory Comput Syst 44, 160–174 (2009). https://doi.org/10.1007/s00224-008-9104-3
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DOI: https://doi.org/10.1007/s00224-008-9104-3