Solving a 4-colored 5-cube puzzle by graph theory

Abstract

Instant Insanity is a puzzle of four cubes where each face of each cube is colored with one of the four colors. The objective of Instant Insanity is to arrange the four cubes in a stack, so that for each of their four long sides (front, back, left and right), each color appears exactly once. In this research, we propose a new puzzle called the 4-colored 5-cube puzzle, which consists of five cubes: the first four cubes are the original cubes from Instant Insanity, and the fifth cube is a copy of one of the four cubes. This puzzle aims to stack the original four cubes and attach the last cube to a face of one of those cubes, forming a structure called a tower, in which each color appears exactly once vertically and horizontally on each side (front, back, left and right). To solve the puzzle, we apply graph theory to construct graphs that represent the arrangement of a tower. We demonstrate all ways of arranging the cubes to solve the puzzle.