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Some thoughts about a proof, that 24 moves suffice

I thought about the number of cosets of H=<U,D,R2,L2,F2,B2> we need to compute to show, that 24 moves suffice.
It is not difficult to show that the number of cosets needes for 24 moves is at most 64430, provided that we get a maximum of 20 moves in each coset (which is quite realistic).