From cube-lovers-errors@mc.lcs.mit.edu Tue Feb 9 15:30:14 1999 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 PAA04382 for ; Tue, 9 Feb 1999 15:30:14 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Sun, 7 Feb 1999 21:18:58 +0000 From: David Singmaster To: reid@math.brown.edu Cc: CUBE-LOVERS@ai.mit.edu Message-Id: <009D3667.F01254DB.8@ice.sbu.ac.uk> Subject: Re: Query on Octagon Cube Edge Parity Problem Similar parity problems can be produced by recolouring a cube. I once sold a cube to someone who came back a few minutes later with two centers exchanged. I accused him of taking it apart, but then I fiddled with it and got it back right, which amazed me even more. Then I discovered that two opposite faces of the cube were colored red! Some time later, I had an example with two adjacent sides having the same color. In 1980, Tamas Varga showed me some cubes with just two colors and I then made up numerous such color variants. E.g. using just two colors, have the three faces of one color meet at an corner, or not meet at a corner (these are the only two ways of coloring the faces with two colors, three faces of each color). Also fun is a three color cube - two opposite sides red, two opposite sides white and two opposite sides blue. Then every corner is red, white, blue - except half of them are red, blue, white. All these are difficult to solve for people who have only done ordinary cubes. In the mid 1980s, Edward Hordern showed me a cube which I recall he said Nob Yoshigahara had invented, but my example was made by Marcel Gillen. This appear to be a 4^3, but when turned, it moves eccentrically. Examination shows that it is a 3^3 with three layers of pieces glued to three adjacent faces. Edward's original example had no colors, so it took some time to solve as one didn't know where pieces went. Further, the eccentric movement causes parts to protrude, making it hard to hold and to move. All in all, a most enjoyable variant. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk