The Instant Insanity Puzzle Jim Cobb Dept. of Mathematics University of Utah March 20, 2019

Fifty years ago a new puzzle appeared Fifty years ago a new puzzle appeared. It consists of four cubes whose faces are colored one of four colors: Red Green Blue White The colors of the left and right faces of the cubes are of no consequence (indeed, except for the left of the first cube and the right of the final one, those faces are hidden). One could call this the Rubik's cube of the sixties because it attracted so much attention and was found to be hard to solve without using some kind of mathematical tool. For this reason, the name under which it was marketed seemed appropriate: Instant Insanity. Objective: Arrange the cubes in a row so that along the front, back, top, and bottom each color appears once among the four cubes.

What makes Instant Insanity so difficult to solve? Each cube has two faces that are irrelevant to the solution It is impossible to see all four relevant faces at the same time We will use a mathematical model that preserves the logical relationship of two faces being opposite each other while losing the geometric information that makes it impossible to see all faces at once. We will use Graph Theory.

1 2 3 4 1 2 3 4

Create Two Subgraphs Each subgraph contains exactly one edge of a particular color Each vertex has exactly two edges No edge is in both subgraphs

3 2 2 4 3 1 1 1 2 4 3 4

1 2 3 4 F➜B T➜B 1 3 2 4 4 3 2 1 4 3 2 1

1 2 3 4 F➜B T➜B 1 3 2 4 4 3 2 1

Source http://www.winning-moves.com/instantinsanitysolution/