From:

~~~ Subject:

Mikko Haapanen <hazard@niksula.hut.fi> writes:

>This reminds me another old question: 3x3x3 are told to have about 4

>trillion (or whatever) different positions. How many of these positions are

>'solved cube' but with different centerpiece combinations? Once i had 3x3x3

>with 6 different pictures (picture/side). Friends asked me to solve it. When

>i was completed, they laughed at me and pointed the bottom center piece,

>which was out of orientation (i can't remember how many of centers were out

>of order).

Actually, I think the 4 "trillion" estimate is ignoring the center orientation.

Let's see:

8! corner positions

x 3^7 corner orientations

x 12!/2 edge positions

x 2^11 edge orientations

= 4.325x10^19

Well, forty-three quadrillion.

Five center orientations force the sixth, so multiply your number by 4^5 to

get the answer 4.429x10^22 positions, counting center piece

orientations. That's 44 quintillion. Whew.

I remember when I solved the 5x5x5 cube (finally), someone asked me if I

had solved the "invisible" 3x3x3 inside it. I'm not sure I even want to

think of trying to solve that. I'll work on the 3x3x3x3 first. :P

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