Ernő Rubik’s 1983 US patent 4,378,116 for a “spatial logical toy,” showing internal mechanisms.

2018

RUBIK’S CUBE ROBOTS

The construction of robots capable of solving a Rubik’s Cube^® using computer vision and physical manipulation has been a popular challenge for AI engineers, who have developed numerous different robotic designs over the years. The original Rubik’s Cube was invented by the Hungarian inventor Ernő Rubik (b. 1944) in 1974; by 1982, 10 million of them had been sold in Hungary (which is, curiously, more than the population of that country). It is estimated that over 100 million have been sold worldwide to date.

The cube is a 3 × 3 × 3 array of smaller cubes that are colored in such a way that the six faces of the large cube have six distinct colors. The twenty-six external subcubes are internally hinged so that these six faces can be rotated. The goal of the puzzle is to return a scrambled cube to a state in which each side has a single color. There are 43,252,003,274,489,856,000 different arrangements of the small cubes, and only one of these arrangements is the initial position where all colors match on each of the six sides. If you had a cube for every one of these “legal” positions, you could cover the entire surface of Earth (including oceans) about 250 times.

In 2010, researchers proved that no starting configuration of the cube requires more than twenty moves to solve. In 2018, an agile Rubik’s Cube robot called the Rubik’s Contraption finally pierced the half-second boundary, solving a scrambled cube in just 0.38 seconds, which included image capture, computation, and movement time. The setup employed by MIT robotics student Ben Katz and software developer Jared Di Carlo made use of six Kollmorgen ServoDisc motors and the so-called Kociemba two-phase algorithm. By comparison, 10.69 seconds was the robotic world record in 2011. Also in 2018, a deep-learning machine finally taught itself how to solve a Rubik’s Cube using reinforcement learning without human knowledge.

One variation that never appeared on toy- store shelves is the four-dimensional version of the Rubik’s Cube: the Rubik’s tesseract. The total number of positions of the Rubik’s tesseract is an astounding 1.76×10¹²⁰. If the rotating layers of either the cube or the tesseract changed positions every second since the beginning of the universe, they would still be turning today and not have exhibited every possible configuration.