A4_1 Atoms Cubed!

Abstract

The Rubik’s Cube is famous for having a large number of permutations to it. We identify how large a Rubik’s Cube would need to be for the number of combinations it has to exactly match the number of atoms in it for various dimensions of the cubes. We found that the 3 × 3 × 3 Rubik’s Cube, which normally has a side length of 5.7 cm ± 1 mm, is the only Cube that would meet this property at the visible scale while still being able to be held. When this Cube fits this given criteria it has a side length of 2.43 mm.