Instant insanity: Uniqueness and existence of solutions

This mathematics research project will probe into the game Instant Insanity, a classic puzzle which involves stacking four cubes whose faces are covered in four colors. This research will attempt to answer four questions: how to solve one specific puzzle layout, how to generalize a solution method that solves other layouts to the puzzle, which conditions lead to the existence or non-existence of a puzzle solution for a layout, and which conditions lead to the uniqueness or non-uniqueness of a puzzle solution for a layout. Research methods include the use of directed graphs, combinatorial objects such as necklaces, multi-sets for categorizing solutions, and the probabilistic analysis of data. This project will illustrate important mathematical concepts such as equivalence classes and pigeonhole principle. It will also offer insights into what makes a puzzle challenging. (Author abstract)