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God's Number is 20

God's Number is 20. R L U2 F U' D F2 R2 B2 L U2 F' B' U R2 D F2 U R2 U Superflip, the first position proven to require 20 moves. God's Number is 26 in the quarter turn metric! Every position of Rubik's Cube™ can be solved in twenty moves or less. One may suppose God would use a much more efficient algorithm, one that always uses the shortest sequence of moves; this is known as God's Algorithm. It took fifteen years after the introduction of the Cube to find the first position that provably requires twent...

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God's Number is 20 | cube20.com Reviews

<META> DESCRIPTION

God's Number is 20. R L U2 F U' D F2 R2 B2 L U2 F' B' U R2 D F2 U R2 U Superflip, the first position proven to require 20 moves. God's Number is 26 in the quarter turn metric! Every position of Rubik's Cube™ can be solved in twenty moves or less. One may suppose God would use a much more efficient algorithm, one that always uses the shortest sequence of moves; this is known as God's Algorithm. It took fifteen years after the introduction of the Cube to find the first position that provably requires twent...

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1 new results

2 date

3 lower bound

4 upper bound

5 notes and links

6 suffice

7 is always sufficient

8 is always enough

9 partitioning

10 symmetry

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God's Number is 20 | cube20.com Reviews

https://cube20.com

God's Number is 20. R L U2 F U' D F2 R2 B2 L U2 F' B' U R2 D F2 U R2 U Superflip, the first position proven to require 20 moves. God's Number is 26 in the quarter turn metric! Every position of Rubik's Cube™ can be solved in twenty moves or less. One may suppose God would use a much more efficient algorithm, one that always uses the shortest sequence of moves; this is known as God's Algorithm. It took fifteen years after the introduction of the Cube to find the first position that provably requires twent...

INTERNAL PAGES

cube20.com

1

God's Number is 26 in the Quarter Turn Metric

http://www.cube20.com/qtm

God's Number is 26 in the Quarter-Turn Metric. U U F U U R- L F F U F- B- R L U U R U D- R L- D R- L- D D Superflip composed with fourspot, the first position proven to require 26 moves. Every position of Rubik's Cube™ can be solved in 26 quarter moves or less. With about 29 CPU-years of idle computer time at the Ohio Supercomputing Center, two researchers have essentially solved every position of the Rubik's Cube™ in the quarter-turn metric, and shown that no position requires more than 26 moves. Michae...

2

Hard Positions

http://www.cube20.com/distance20s

Known Distance-20 Positions in the Half-Turn Metric. All 93,659,370 known distance-20 positions as of 18 March 2014 are available below. Calculating the symmetry of each scramble, and the various distinct positions represented, is left as an exercise. Before you download the large (11MB) file you might try downloading random10.txt. Containing 10 randomly selected, positions, or random100.txt. The data file htm.zip. Known Distance-24 or Greater Positions in the Quarter-Turn Metric. In addition, we present...

3

Cube Programs

http://www.cube20.com/src

Sources for Coset Solver and Two-Phase Solver. These sources compile and run on linux. They should also compile and run on a sufficiently large Windows machine. They require pthreads. They are written in a literate programming style using the CWeb system. You will need cweave to compile the programs. Cubepos provides the basic definitions of the cube group and standard utility functions such as reading and writing positions, parsing moves, executing moves, calculating inverses, and more.

4

Rubik's Clock

http://www.cube20.com/clock

Rubik's Clock has now been solved! Inspired by the optimal solvers written by a number of people, and Jakob Kogler's surprising proof of God's Number (12), I decided see how well a "coset solver" would work on this problem. It turns out, surprisingly well! 0 1 1 330 2 51,651 3 4,947,912 4 317,141,342 5 14,054,473,232 6 428,862,722,294 7 8,621,633,953,202 8 101,600,180,118,726 9 528,107,928,328,516 10 613,251,601,892,918 11 31,893,880,879,492 12 39,248 - - - - - - - - - - - - 1,283,918,464,548,864.

5

CubeLovers Mailing List

http://www.cube20.com/cubelovers

CubeLovers was a mailing list dedicated to the mathematics of Rubik's Cube and similar puzzles active from 1980 to 1999. The mailing list lives on in forum form here. In order to preserve the original fascinating material, I am making a copy of the archive here for people to peruse. The dates, authors, and titles of each posting are available in one big list here,. With each line clicking through to the message itself. The original files as made available after the mailing list shut down are listed here:.

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God's Number is 20

God's Number is 20. R L U2 F U' D F2 R2 B2 L U2 F' B' U R2 D F2 U R2 U Superflip, the first position proven to require 20 moves. God's Number is 26 in the quarter turn metric! Every position of Rubik's Cube™ can be solved in twenty moves or less. One may suppose God would use a much more efficient algorithm, one that always uses the shortest sequence of moves; this is known as God's Algorithm. It took fifteen years after the introduction of the Cube to find the first position that provably requires twent...

cube20.org

God's Number is 20

God's Number is 20. R L U2 F U' D F2 R2 B2 L U2 F' B' U R2 D F2 U R2 U Superflip, the first position proven to require 20 moves. God's Number is 26 in the quarter turn metric! Every position of Rubik's Cube™ can be solved in twenty moves or less. One may suppose God would use a much more efficient algorithm, one that always uses the shortest sequence of moves; this is known as God's Algorithm. It took fifteen years after the introduction of the Cube to find the first position that provably requires twent...

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Or the Hungarian cube has drawn attention, and has received the broadest distribution. Rubik's Cube (commonly misspelled rubix, . Rubick's or rubics cube) is a Mechanical puzzle invented by Erno Rubik's.We shall try to tell about how to put in order the mixed Rubik's Cube.In 1977 Erno Rubik's most original of all puzzles was patented. Rubik's Revenge), and the 5 5 5. Accepted system of designations: sides of a Rubik's Cube are designated by letters F, B, R, L, U, D. F-r, r-u, f-d. The letter C (center).

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