Tom Rokicki - Twenty Moves Suffice for Rubik's Cube - CoM January 2024 скачать в хорошем качестве

Tom Rokicki - Twenty Moves Suffice for Rubik's Cube - CoM January 2024

Twenty Moves Suffice for Rubik’s Cube Despite having 43,252,003,274,489,856,000 different positions, the Rubik’s cube can always be solved in 20 moves or less. This result, known as God’s number, was finally proved more than 30 years after the invention of the cube. We present some history of the mathematical and computational exploration of the cube, highlighting Kociemba’s amazing subgroup-based algorithm that calculates near-optimal solutions. We turn this algorithm inside-out, to solve an entire coset of positions at the same time, enabling resolution of the diameter of the cube group with a reasonable amount of computation. We give some details of the effort and finally close with some recent results and open questions.