From cube-lovers-errors@oolong.camellia.org Tue Jun 3 14:52:43 1997
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Date: Tue, 03 Jun 1997 06:13:22 EDT
From: Richard M Morton RMM - ICOMSOLS
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Subject: Number of States for 2x2x2 cube
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Reading about the number of possible states (88million) for the corners
of the 3x3x3 cube (equiv. to 2x2x2) made me try working this out for
myself. My logic was :
Cube has 8 corners, each of which can have 3 orientations. Number of
possible states is
(8*3)*(7*3)*(6*3)*(5*3)*(4*3)*(3*3)*(2*3)*(1*3) = 8!*3**8 = 264,539,520
This figure of course includes some states only possible by disassembling
the cube (or maybe by twisting it in a fourth dimension ?). Without this
the last corner can only have one orientation so the number of states
achievable by twisting only in 3d is 8!*3**7 = 88179840
I assume that this is the correct figure but what I would like to know is
whether my logic is correct ie is the assumption about the last corner
being fixed in orientation the only requirement (I am not a mathematician
so please excuse me if this is obvious).
Richard Morton "I'm Brian and so's my wife"