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Date: 15 Sep 1980 1842-PDT From: Alan R. Katz <KATZ at USC-ISIF>I have seen the number 4.3 * 10^19 for the number of reachable states

for the cube, can anyone tell me how you calculate it? This may have

been answered before in this list, but I couldn't find it.Also, someone mentioned that one can make a checkerboard pattern from

the Pons Asinorum by trebly rotating the centers by a simple

transformation. Can anyone tell me this transformation? (again I may

have missed reading it)

Reply to either me or the list.Alan -------

Consider the corners. There are 8 of them, and they can go

anyplace. This leads to 8 factorial permutations. Each corner can

take on three orientations, so this is another factor of 3^8. But

the corners have three possible states (trarity [three way

parity]) so divide by 3. Now do the same with the edges. 12 edges

gives 12 factorial arrangements, times 2^12 oreintations. But the

edges have two parities involved, so divide by four (thus giving

rise to the 12 states of the cube, one of which has the solved

configuration as a member). So if you evaluate

8 12 8!*3 *12!*2 ----------- 3*4

you will get 4.3 * 10^19.