From cube-lovers-errors@mc.lcs.mit.edu Tue Feb 9 15:30:14 1999
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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