**Reference**:- Tetsuo Asano, Erik D. Demaine, Martin L. Demaine, and Ryuhei Uehara, “Kaboozle is NP-complete, even in a Strip”, in
*Proceedings of the 5th International Conference on Fun with Algorithms (FUN 2010)*, Lecture Notes in Computer Science, volume 6099, Ischia, Italy, June 2–4, 2010, pages 28–36. **Abstract**:- 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.
**Comments**:- This paper is also available from SpringerLink.
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**Related papers**:- Kaboozle_JIP (NP-completeness of generalized Kaboozle)

See also other papers by Erik Demaine.

Last updated July 21, 2021 by Erik Demaine.