I've been attempting to use the 'method' Singmaster offers in his 5th
edition pamphlet for solving my cube, and have arrived at an
undocumented position. Perhaps I'm overlooking something and a
cubeophile out there can offer an explanation of where I'm going
wrong. I have reached the position described after step 6 just before
proceeding to step 7. The bottom and top faces are one color, the
center slice cubies are corrrectly colored and the upper edge cubies
(the + pattern) are correctly oriented. Two of the upper adjacent
corners are correctly oriented but the opposite two are not. At this
point Singmaster deals with putting the rest of the U corners in their
correct slots although not orienting them correctly necessarily. If we
represent my U corners with

1	2

3	4

then the cubies want to be rearranged as follows

1 and 2 want to be exchanged

I don't see any way of getting this operation out of the cases
documented by Singmaster. What gives?
-------