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Subject:

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.]

--- --- -0-- --- --- --- -- -- --- --- --- --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --- -- -- -- -- -- -- -- -- -- -- -- --

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