# The Mathematics of a Rubik’s Cube

Rubik’s cubes are ubiquitous in modern culture. This immensely popular puzzle toy was first invented in 1974 by a Hungarian sculptor named Ernő Rubik, and it became an international success in the early 1980s. The Rubik’s Cube enjoyed a resurgence in popularity in the mid-2000s and has been a cultural icon. Hungarians are incredibly proud that this world-famous toy originated in their country. I saw several depictions of the Rubik’s Cube around Budapest during my travels there.

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As fun and popular as the Rubik’s Cube is, there is much more going on under the surface. Mathematician David Singmaster was quick to notice how the Rubik’s Cube had significant connections to math. The various arrangements and permutations of the cube’s faces make it a rich landscape for mathematical investigation. In fact, there are over 43 quintillion different orientations of the Rubik’s Cube! That is 43 with 15 zeros behind it. This means every time you see a new scrambled…