Every position of Rubik’s Cube can be solved in 20 moves or less

You need to know: Rubik’s Cube

Background: A move in the Rubik’s Cube is defined as any twist of any face. By solution of a position of Rubik’s Cube we mean the sequence of moves after which each face of Rubik’s Cube has only one colour.

The Theorem: On 24th February 2012, Tomas Rokicki, Herbert Kociemba, Morley Davidson, and John Dethridge submitted to the SIAM Journal on Discrete Mathematics a paper in which they gave an exposition of their computational proof that every starting position of Rubik’s Cube can be solved in 20 moves or less.

Short context: Rubik’s Cube, invented by Ernő Rubik in 1974, is widely considered to be the world’s best-selling toy. The least integer n such that every position can be solved in at most n moves is known as God’s number. The problem of determining the God’s number (let us denote it $g$ ) has been of interest ever since the Rubik’s Cube is invented. A simple counting argument proves that $g\geq 18$ . The first upper bound $g\leq 52$ was proved by Thistlethwaite in 1981. Then many researches proved better and better lower and upper bounds. The Theorem culminates this line of research and determines the God’s number exactly: $g=20$ .