Kaboozle Is NP-complete, even in a Strip
Author(s)Asano, Tetsuo; Demaine, Erik D.; Demaine, Martin L.; Uehara, Ryuhei
MetadataShow full item record
Kaboozle is a puzzle consisting of several square cards, each annotated with colored paths and dots drawn on both sides and holes drilled. The goal is to join two colored dots with paths of the same color (and fill all holes) by stacking the cards suitably. The freedoms here are to reflect, rotate, and order the cards arbitrarily, so it is not surprising that the problem is NP-complete (as we show). More surprising is that any one of these freedoms—reflection, rotation, and order—is alone enough to make the puzzle NP-complete. Furthermore, we show NP-completeness of a particularly constrained form of Kaboozle related to 1D paper folding. Specifically, we suppose that the cards are glued together into a strip, where each glued edge has a specified folding direction (mountain or valley). This variation removes the ability to rotate and reflect cards, and restricts the order to be a valid folded state of a given 1D mountain-valley pattern.
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Fun with algorithms (International Conference) / Lecture notes in computer science
Tetsuo, Asano, et al. "Kaboozle is NP-complete, even in a strip" Fun with algorithms, 2010. (Lecture notes in computer science ; v. 6099)28-36. Copyright © 2010, Springer
Author's final manuscript