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A257401
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God's number for a Rubik's cube of size n X n X n (using the half turn metric).
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2
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OFFSET
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1,2
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COMMENTS
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"God's Number" is the maximum number of turns required to solve any scrambled cube. The "Half turn metric" considers a 90- or 180-degree turn of any side to be a single turn. The number is not known for cubes of size larger than 3 X 3 X 3.
God's number has been proved using a brute-force attack for the 2 X 2 X 2 and 3 X 3 X 3 cubes. For the 4 X 4 X 4 cube, it has been proved only that the lower bound is 31, while the most probable value is considered to be 32; solving this by brute force would require checking all the A075152(4) possible permutations of the "Master Cube". - Marco Ripà, Aug 05 2015
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LINKS
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Table of n, a(n) for n=1..3.
Jerry Bryan, God's Algorithm for the 2x2x2 Pocket Cube
Joseph L. Flatley, Rubik's Cube solved in twenty moves, 35 years of CPU time
Tomas Rokicki, Herbert Kociemba, Morley Davidson, and John Dethridge, The Diameter Of The Rubik's Cube Group Is Twenty, SIAM J. of Discrete Math, Vol. 27, No. 2 (2013), pp. 1082-1105.
Jaap Scherphuis, Mini Cube, the 2×2×2 Rubik's Cube
Speedsolving.com, Rubik's Cube Fact sheet
Wikipedia, Optimal solutions for Rubik's Cube
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CROSSREFS
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Cf. A256573 (quarter turn metric), A054434 (possible positions), A075152 (possible permutations).
Cf. A079761, A079762, A080601, A080602.
Sequence in context: A129909 A174976 A003284 * A283903 A063589 A102815
Adjacent sequences: A257398 A257399 A257400 * A257402 A257403 A257404
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KEYWORD
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nonn,hard,more,bref
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AUTHOR
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Peter Woodward, Apr 21 2015
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STATUS
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approved
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