From: Jerry Bryan
Subject: Re: 4x4x4 solution
To: C.McCaig@Queens-Belfast.AC.UK
Cc: cube-lovers@ai.mit.edu
On Tue, 30 Sep 1997 C.McCaig@Queens-Belfast.AC.UK wrote:
> i recently borrowed a friends 4x4x4, and i know the basic method for
> solving it. ie get the 6 centres, pair up all the edges, and then
> solve for the normal cube. however, about half the time i end up
> with a single edge pair inverted and cant figure out a move for
> reorientating the single edge pair. usually i break a few pairs
> and try and reorientate them this way, but this seems rather longwinded...
> does anyone have a move for this?. for example, say the green edge
> is on the blue face, and the blue edge is on the green face...
>
Your problem is one of parity. You have two edges cubies swapped (this
swap is visible) and two face center (centre) cubies of the same color
swapped (this swap is invisible). You have to have an even number of
swaps in the total cube. If you want an even number in the edges (and
you do), then you also have to have an even number in the face centers,
even if swaps in the face centers are invisible.
There is probably a more elegant solution, but the following will work.
If you encounter the situation you describe, make any middle slice
quarter turn. This will disturb the centers. The centers will now have
an even numbers of swaps. Solve the centers again without simply undoing
the middle slice you just made. The parity of the edges will then be
ok. (I'm assuming that your solution for the face centers will maintain
their parity after you correct it as described.)
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us
Pellissippi State (423) 539-7198
10915 Hardin Valley Road (423) 694-6435 (fax)
P.O. Box 22990
Knoxville, TN 37933-0990
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