Date: Sat, 06 Apr 96 15:36:52 -0400
From: Nichael Lynn Cramer <nichael@sover.net >
Subject: Re: Square-1 question

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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-0--
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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
```