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2008

Twenty-Five Moves Suffice for Rubik's Cube

Rokicki, Tomas

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Understand

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.

Twenty-Five Moves Suffice for Rubik's Cube · Around

Built on

Kociemba, Herbert. “Close to God’s Algorithm” Cubism For Fun
1992
Earlier work this paper cites.
Reid, Michael. “New upper bounds.” cube-lovers e-mail, January 7, 1995
1995
Earlier work this paper cites.

Similar

Reid, Michael. “Superflip requires 20 face turns.” cube-lovers e-mail, January 18, 1995
1995
Cited alongside, same era.
Kociemba, Herbert. Cube Explorer (Windows program). http://kociemba.org/cube.htm
Cited in the paper.
Kunkle, D.; Cooperman, G. “Twenty-six Moves Suffice for Rubik’s Cube.” Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC ’07)
Cited in the paper.
Korf, Richard E. “Finding Optimal Solutions to Rubik’s Cube Using Pattern Databases.” Proceedings of the Workshop on Computer Games (W31) at IJCAI-97
Cited in the paper.
Radu, Silviu. “New Upper Bounds on Rubik’s cube.” http://www.risc.uni-linz.ac.at/ publications/download/ risc_3122/uppernew3.ps
Cited in the paper.

Then

Rokicki, Tomas. “In search of: 21f*s and 20f*s; a four month odyssey.” 7 May 2006. http://cubezzz.homelinux.org/ drupal/?q=node/view/56
2006
Later among the works it cites.

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