From:

Subject:

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.

The number is (12! * 2^12 * 8! * 3^8)/12. This comes from the following.

There are 8 corners and there are 3 positions- hence 8!*3^8. There are

12 edges with 2 positions hence 12!*2^12. Finally, the /12 comes from

parity considerations. Only 1/4 of the positions in the flippling of

two edges are possible while 1/3 of the toppling of two edges are possible.

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)

The moving of centers is easy- 4 moves of the center slice while rotating

the cube 90 degrees in your hand between moves. With the transformation

in hand you can move the centers easily to possible positions.