[next] [prev] [up] Date: Wed, 23 Nov 94 17:02:26 -0500
[next] [prev] [up] From: Jerry Bryan <BRYAN@wvnvm.wvnet.edu >
~~~ ~~~ [up] Subject: <U,R> Q vs. Q+H Distance to Start -- All Positions

This is the same chart as before except that it is in terms of all
cube positions in <U,R> rather than in terms of W-conjugacy classes.

At the same time, I will take the opportunity to correct an error
in the previous posting. Permitting Q+H moves rather than just
Q moves can save up to 10 moves (e.g., 25 moves with Q and 15 moves
with Q+H, 24 moves with Q and 14 moves with Q+H, and 22 moves with
Q and 12 moves with Q+H). My thanks to Dan Hoey for spotting this error.

Q+H Distance from Start

      0 1 2  3  4   5   6    7    8     9    10    11     12     13      14
    0 1
    1   4
    2   2 8
Q   3     8 16
    4     2 24 32
D   5       12 64  64
i   6        2 48 160 128
s   7          16 160 384  256
t   8           2  80 480  896  512
a   9              20 320 1344 2048  1024
n  10               2 120 1120 3584  4590  2032
c  11                  24  560 3552  9168 10128  4016
e  12                   1  164 2232 10519 22736 21820   7788
   13                       20  880  7904 29732 54624  46332  14700
f  14                           192  3904 25890 80606 128248  96324   25528
r  15                            16  1184 15238 79970 210684 293572  187112
o  16                                 177  5900 54398 234536 536474  641412
m  17                                  12  1280 25164 181514 663960 1310584
   18                                       150  7192  96478 564998 1791466
S  19                                         8  1072  31288 321242 1613572
t  20                                              58   5186 107919  902990
a  21                                                    296  17192  269272
r  22                                                      1    592   32122
t  23                                                                   782
   24                                                                     8
   25

Q+H Distance from Start

           15      16      17      18    19 20
    0
    1
    2
Q   3
    4
D   5
i   6
s   7
t   8
a   9
n  10
c  11
e  12
   13
f  14
r  15   39764
o  16  328532   49916
m  17 1286534  464878   34914
   18 2960340 2069994  393142    8230
S  19 4333614 5277159 1974444  107256   166
t  20 3846819 7828346 5215618  562494  2252
a  21 1881664 6123940 6933978 1349768 10712
r  22  405221 2181984 4071140 1328952 19411 32
t  23   23010  232088  779418  462831 12969 12
   24      92    2714   18612   23981  1936  8
   25       2               8      56    19  2


 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Robert G. Bryan (Jerry Bryan)              (304) 293-5192
Associate Director, WVNET                  (304) 293-5540 fax
837 Chestnut Ridge Road                     BRYAN@WVNVM
Morgantown, WV 26505                        BRYAN@WVNVM.WVNET.EDU

If you don't have time to do it right today, what makes you think you are
going to have time to do it over again tomorrow?


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