Message #146

From: guy_padfield <>
Subject: Cubes, beer and Beethoven
Date: Thu, 05 May 2005 19:05:23 -0000

My solutions of the 3^4 and 4^4 are probably the least elegant and
most long-winded of anyone’s. Instead of wracking my brains for the
shortest way to bring 3 distant pieces into alignment and
orientation and memorising cunning preliminary moves, I sit back at
the computer with a beer, chewing on a pipe and listening to
Beethoven, gently reversing entropy with minimum energy expenditure.
In terms of time, this is actually quite a quick method (and very
enjoyable), but the solution files are horrific.

When I embarked upon the 5^4 in the same spirit I met a new problem -
I can’t see all the interior cubies without twisting the cube back
and forth and find myself peering at the computer screen like an old
lady looking for her glasses. The perspective distortion also means
I often mistake their positions. The notes say you can change the
size of the cubies with a command line but being unfamiliar with
Linux I don’t know how to do this (I am using Knoppix). Does making
them smaller increase the transparency of the faces and make this
easier? If so, how do I do this (answers phrased for a graduate of
philosophy/ancient languages rather than maths/IT please)?

I have much enjoyed the mathematical discussions on this site
recently, particularly concerning the question of whether the
available rotations would be physically possible in a ‘real’ 4D cube
(my conclusion, like yours I think, is that they would). Could the
mathematicians answer another question, relating to the 4^4? In the
3D version there are two independent parity problems if you follow
the ‘ultimate solution’: the last pair of edges is inverted 50% of
the time, resolvable by reconstructing the faces and the last two
corners are switched 50% of the time, resolvable by reconstructing
the edges. I guessed there might be three parity problems in the
4^4: that the faces would only be realisable if the centres were
correct, the edges only if the faces were and the corners only if
the edges were. When I solved it I met just one of these problems: I
had three intractably inverted edge cubies and found they dropped
into place only after I had re-aligned the faces (I switched the
position of a pair of adjacent face pieces on two separate sides).
The corners were right. Was I lucky? I don’t propose to test this
empirically, for obvious reasons.

Would a layer by layer solution, as Marc Guegueniat has found,
remove the parity issues?

Guy Padfield