The Four Cube Problem

The four cube problem is a mathematical puzzle that involves four cubes. The cubes are placed on a flat surface so that each face of each cube is touching the face of exactly one other cube. The goal of the puzzle is to arrange the cubes in a way such that each face of each cube is touching the face of a different color.

To solve the four cube problem, the first step is to find the cube that has a face of each color. This cube is known as the “key cube.” Once the key cube has been identified, the other three cubes can be arranged around it so that each face of each cube is touching the face of a different color.

One way to solve the four cube problem is to first arrange the cubes in a 2×2 square, with the key cube in the upper left corner. The other three cubes can then be arranged around the key cube so that each face of each cube is touching the face of a different color.

Another way to solve the four cube problem is to first arrange the cubes in a line, with the key cube in the middle. The other three cubes can then be placed on either side of the key cube so that each face of each cube is touching the face of a different color.

Regardless of which approach is used, the key to solving the four cube problem is to carefully identify the key cube and then carefully arrange the other three cubes around it. With practice and persistence, anyone can learn to solve the four cube problem.

Another presentation by Robin Wilson, Gresham Professor of Geometry, this clip explains the four cube problem and how to solve it. Many more explanations of various puzzles can be found on the Gresham College website.

How might solving a problem like this relate to the concepts of insight and trial and error? What is the Gestalt approach to problem solving?