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Date: Mon, 26 Oct 1998 23:58:27 -0400 (EDT)
From: Jerry Bryan
Subject: 12q From Start
To: Cube-Lovers
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|x| Patterns Lcl Positions Lcl Branching
Max Max Factor
0q 1 0 1 0
1q 1 0 12 0 12
2q 5 0 114 0 9.5
3q 25 0 1068 0 9.368
4q 219 0 10011 0 9.374
5q 1978 0 93840 0 9.374
6q 18395 0 878880 0 9.366
7q 171529 0 8221632 0 9.355
8q 1601725 0 76843595 0 9.347
9q 14956266 0 717789576 0 9.341
10q 139629194 4 6701836858 42 9.337
11q 1303138445 0 62549615248 0 9.333
12q 12157779067 103 583570100997 2913 9.330
The last time a new level was calculated for the quarter turn metric was 4
February 1995.
The cumulative number of positions now identified is 653625391832, or
about 6.5*10^11. This is well past the "geometric halfway point" of
sqrt(|G|), which is about 6.5*10^9. However, it is known that the
diameter of G is at least 26q, strongly indicating that there is a bit of
a tail to the distribution of positions by length.
Of the 103 local maxima of length 12q, 70 of them also have their inverse
as local maxima. For the other 33, the inverse is not a local maximum.
For one of them, the inverse has 11 moves which go closer to Start. For
seven of them, the inverse has 10 moves which go closer to Start. For
eleven of them, the inverse has 8 moves which go closer to Start. For six
of them, the inverse has 6 moves which go closer to Start. For two of
them, the inverse has 4 moves which go closer to Start. And for six of
them, the inverse has only 2 moves which go closer to Start.
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us