Last August, 30 years after the Rubik’s cube first appeared, an international team of researchers proved that no matter how scrambled a cube got, it could be solved in no more than 20 moves. Although ...

Take two positive whole numbers that are both less than 20. The difference in the squares of these numbers is a perfect cube and the difference in their cubes is a perfect square. (Perfect means that ...

If you suspend a Rubik’s Cube near the corner of a room and shine lights at its exposed faces, it will cast square shadows on two walls and the floor. A real-world Rubik’s Cube has a gadget at its ...

In 2010, an international team of researchers proved that no matter how scrambled a Rubik’s cube got, it would require no more than 20 moves to solve it. Their proof, however, relied on the equivalent ...