A257401 -id:A257401 - cp's OEIS frontend

A256573 God's number for Rubik's cube size n X n X n (quarter-turn metric).

0, 14, 26

Offset: 1

Peter Woodward, Apr 22 2015

"God's Number" is the maximum number of turns required to solve any scramble of cube. "Quarter-turn metric" considers a 90-degree turn of any side to be a single turn, while a 180-degree turn is considered two turns. Cubes of larger size than 3 X 3 X 3 are not solved for God's number.

Jerry Bryan, God's Algorithm for the 2x2x2 Pocket Cube
Tomas Rokicki, Morley Davidson, God's Number is 26 in the Quarter-Turn Metric

Cf. A257401 (half-turn metric), A054434 (possible positions), A075152 (possible permutations).

A330389 Maximal order of an element in the n X n X n Rubik's cube group.

Original entry on oeis.org

45, 1260, 765765, 281801520, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880, 5354228880

Offset: 2

Dmitry Kamenetsky, Dec 13 2019

nonn

For the standard Rubik's cube (n = 3) the longest period 1260 is obtained with the moves RU2D'BD'.

a(n) = a(6) for all n > 6.

Math StackExchange, Determine the highest order of an element of a Rubik's Cube group.
Puzzling StackExchange, Worst way to solve Rubik's in one algorithm.

Cf. A007458, A054434, A075152, A257401.

cp's OEIS Frontend

A256573 God's number for Rubik's cube size n X n X n (quarter-turn metric).

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