[next] [prev] [up] Date: Sat, 07 Oct 95 23:54:00 -0500
[next] [prev] [up] From: Mark Longridge <mark.longridge@canrem.com >
[next] ~~~ [up] Subject: Using 5 Generators

From: "Jerry Bryan" <BRYAN@wvnvm.wvnet.edu>
Subject: <F,U,L,R,D> Question

It is well known that if we define G=<Q> for the twelve quarter turns
q in Q, we can also generate G as G=<F,U,L,R,D>, leaving out B and B'.
Leaving out any other quarter turn would do as well, but I
am going to stick to leaving out B for illustrative purposes.

However, when one of the quarter turns is left out, the length of most
positions will change. In particular, we will no longer have |B|=1.
My reading of the archives indicates that we do not know what the
length of B would be in this situation, nor what a minimal process
for B would be.

This problem was solved by David Benson in Oct. 1979, who was one of
the earliest cube pioneers. Dr. Singmaster reports on this in his
2nd Addendum of "Notes".

Let A = R1 L3 F2 B2 R1 L3, then AUA = D1

AUA = R1 L3 F2 B2 R1 L3 U1 R1 L3 F2 B2 R1 L3   (17 q, 13 q+h)

Perhaps Jerry will find something shorter.

-> Mark <-

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