From cube-lovers-errors@mc.lcs.mit.edu Mon Nov 23 16:35:08 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA19314 for ; Mon, 23 Nov 1998 16:35:06 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <001e01be155b$9a456940$6bc4b0c2@home.icl.web> From: roger.broadie@iclweb.com (Roger Broadie) To: "cube" Cc: "Jorge E. Jaramillo" Subject: Re: The Cylinder Date: Sat, 21 Nov 1998 14:29:22 -0000 I was given a cylinder here in England in 1981. I no longer have the packaging, but I suspect it was Taiwanese, unless the Hungarians made this variant. It was my first cube puzzle, and its shape was so unappealing when disturbed that I put it on one side and got a genuine cube to learn on - well, almost genuine: it came from a street trader in Regent Street. The apparently impossible state is a monoflip of a top or bottom edge piece. There will be a matching flip of a middle-layer edge piece, but that will be invisible, since the piece has only one face. I wondered if it would be possible to get the puzzle into the solved shape and then restore the positions of the pieces without losing the shape, that is, only allowing turns from the group , where S and A are slice and anti-slice moves of the middle layers (I needed them). In fact it is not. There may always be a hidden flip in the middle layer and you can't correct that without moving the piece out of the middle layer, which needs a turn like F, and that destroys the shape. But if you cheat a little and make sure the flips are got right before the shape is finally restored, then it can be done. Andy Southern has already made the point about the flips. He also pointed out that the configuration is not unique because columns corresponding to the vertical edges on a normal cube can be swapped. As a rider to that point, the pretty pattern stripes on the normal cube is not distinguishable on the octagonal prism, because it's striped already. It should be possible to work out whether our moderator's puzzle came in the form he now has by counting stickers. The octagonal prism has 2 sets of 9 (the top and bottom) and 8 of 3 (the side columns). If I've grasped his configuration correctly, if it came in that form originally it should have 4 sets of 6 and 6 of 3. Roger Broadie [ Yes, my decahedron's stickers are incompatible with an octagonal prism solution. I just can't remember whether I replaced some of the stickers to make this new shape. --Dan ]