qqwref
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- Dec 18, 2007
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If you count 1-cycles (solved pieces) as a cycle, they follow the Stirling numbers of the first kind, so e.g. for 5 pieces you have 24 permutations with one cycle (i.e. a 5-cycle), 50 with two, 35 with three, 10 with four, and 1 with five (i.e. five one-cycles, or solved). I'm not sure how thiese numbers change when you don't count 1-cycles as cycles.What's the probability distribution for numbers of edge cycles in a random solve, excluding edge flips? What about corners?