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 ------------------------------ End of Cube-Lovers Digest *************************