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Date: Sat, 12 Sep 1998 13:01:52 -0400 (EDT)
From: Jerry Bryan
Subject: Weak Local Maxima, 6f from Start
To: Cube-Lovers
Reply-To: Jerry Bryan
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I finally have had enough time to add support to my God's Algorithm
program to calculate weak local maxima. The shortest strong local maximum
in the face turn metric is 9f, but the shortest weak local maximum has not
previously been verified. It has long been known that Pons Asinorum is a
weak local maximum at 6f from Start. I have been curious to know if Pons
is the shortest, and if there are any other short weak local maxima.
It turns out that 6f is indeed the shortest. There are two such positions
unique to symmetry which are 6f from Start, the Pons and one other. The
other one is quite pretty:
L2 R2 D2 U2 B' F (6f*)
The eighteen neighbors are as follows.
L2 R2 D2 U2 F2 B' (6f*)
L2 R2 D2 U2 F (5f*)
B' F L2 R2 D2 U' (6f*)
B' F L2 R2 D' U2 (6f*)
B' F D2 U2 L2 R' (6f*)
B' F D2 U2 L' R2 (6f*)
L2 R2 D2 U2 B' (5f*)
L2 R2 D2 U2 B2 F (6f*)
B' F L2 R2 D2 U (6f*)
B' F L2 R2 D U2 (6f*)
B' F D2 U2 L2 R (6f*)
B' F D2 U2 L R2 (6f*)
L2 R2 D2 U2 B' F' (6f*)
L2 R2 D2 U2 B F (6f*)
B' F L2 R2 D2 (5f*)
B' F L2 R2 U2 (5f*)
B' F D2 U2 R2 (5f*)
B' F D2 U2 L2 (5f*)
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us
Pellissippi State (423) 539-7198
10915 Hardin Valley Road (423) 694-6435 (fax)
P.O. Box 22990
Knoxville, TN 37933-0990