From nichael@sover.net Sun Apr 7 15:36:20 1996 Return-Path: Received: from maple.sover.net by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA10461; Sun, 7 Apr 96 15:36:20 EDT Received: from [204.71.18.82] (st32.bratt.sover.net [204.71.18.82]) by maple.sover.net (8.7.4/8.7.3) with SMTP id PAA09328; Sun, 7 Apr 1996 15:36:09 -0400 (EDT) Message-Id: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Sat, 6 Apr 1996 15:36:52 -0400 To: Aaron Weintraub , cube-lovers@ai.mit.edu From: nichael@sover.net (Nichael Lynn Cramer) 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.] --- --- -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