Exploring Properties of the Instant Insanity Puzzle with Constraint Satisfaction Approach

The Instant Insanity Puzzle is a challenging and interesting puzzle of combinatorial nature. The puzzle consists of four different cubes where each face of each cube has one of the four colors red, green, white and blue. The goal is to arrange the cubes in a tower with dimensions 1 x 1 x 4 such that on each of the four long sides of the tower, every color appears exactly once. In this paper we pose questions derived from the puzzle, but with increased difficulty and generality. Amongst other things, we try to find a new problem instance (a new color assignment for the cubes) such that the number of solutions of the instant insanity puzzle is minimized but not null. In addition, we also present a constraint programming model for the proposed questions, which can provide the answers to our questions. The purpose of this paper is on the one hand to share our results over the instant insanity puzzle, and on the other hand to share our gained knowledge on finding problems by constraining the solutions of constraint satisfaction problems, which is (amongst other things) useful for the generation of test data and teaching material.