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About 490 million positions are at distance 20
Submitted by rokicki on Sat, 09/14/2013 - 13:43.Even though we now know the diameter of Rubik's Cube group in the half-turn
metric, there is still much yet to be discovered. The diameter in the QTM
and the STM are unproved (although they are almost certainly 26 and 18,
respectively). The exact count of positions at distance 16, 17, 18, 19,
and 20 in the half-turn metric is unknown. This note reports some progress
on an estimate for the count of 20's in the half-turn metric.
It is fascinating to me how problems of distinctly different difficulty
exist around the 3x3x3 cube in the half-turn metric. Initially, back in
the early days, we could solve individual positions non-optimally.
metric, there is still much yet to be discovered. The diameter in the QTM
and the STM are unproved (although they are almost certainly 26 and 18,
respectively). The exact count of positions at distance 16, 17, 18, 19,
and 20 in the half-turn metric is unknown. This note reports some progress
on an estimate for the count of 20's in the half-turn metric.
It is fascinating to me how problems of distinctly different difficulty
exist around the 3x3x3 cube in the half-turn metric. Initially, back in
the early days, we could solve individual positions non-optimally.
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