At 4:41 PM 4/5/96, Aaron Weintraub wrote:
>Hi...
>
>I recently got a hold of a Square-1 puzzle and have been trying to solve it.
>I can get to the point where it's done, but two edges on one side are
>swapped. How do I swap them back? Is this a parity problem? Every move I
>have that swaps edges does TWO pairs are a time, so I can't get there with
>what I have. Or can I? Any help would be appreciated.
>
>-Aaron

The quick answer is, yes, in spite of appearances you are actually very far
from finished.

A quick hint is attached below. (This is only a hint in that it's been two
or three years since I worked with a Square One. At that time I kept notes
and was going to write up a complete solution but I don't think I ever got
around to doing it [Alan? Do you remember?] If I can find those, or can
remember more complete details --time to get the Sq1 back out-- I'll pass
along more details.]

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Hint: You're right that you need to swap two pairs together. The issue
here is that you need to simultaneously swap a pair of edges (the
triangular pieces) and a pair of corners (the quadrilaterals). And, yes,
you can actually do this. ;-)

In short, in this state the corners only _appear_ to be in the correct
locations.

An analoguous case can occur on the 4X cube where the cube appears to be
_almost_ complete except that two edge peices are flipped. Again, it looks
like you're close to done, but more accurately you're almost completely
diametrically "across the space of solutions".

Nichael
nichael@sover.net                                               __
http://www.sover.net/~nichael              Be as passersby   -- IC