Twenty-Five Moves Suffice for Rubik's Cube

Abstract: How many moves does it take to solve Rubik's Cube? Positions are known that require 20 moves, and it has already been shown that there are no positions that require 27 or more moves; this is a surprisingly large gap. This paper describes a program that is able to find solutions of length 20 or less at a rate of more than 16 million positions a second. We use this program, along with some new ideas and incremental improvements in other techniques, to show that there is no position that requires 26 moves.