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Lower Bounds for n x n x n Rubik's Cubes (through n=20) in Six Metrics
Submitted by rokicki on Mon, 07/18/2011 - 22:12.In January 1981, Dan Hoey posted to cube-lovers a description of a
technique to compute a lower bound on God's Number. This technique
considered the maximum number of positions that can be reached by what
is called "syllables"---consecutive moves on the same axis, possibly
turning distinct faces. Since all the moves that make up a syllable
commute, we can select a single canonical move sequence to represent
every syllable, and then determine how many move sequences of a given
total length can be made out of only these syllables. This gives a
more accurate bound on God's Number because it eliminates many
technique to compute a lower bound on God's Number. This technique
considered the maximum number of positions that can be reached by what
is called "syllables"---consecutive moves on the same axis, possibly
turning distinct faces. Since all the moves that make up a syllable
commute, we can select a single canonical move sequence to represent
every syllable, and then determine how many move sequences of a given
total length can be made out of only these syllables. This gives a
more accurate bound on God's Number because it eliminates many
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