I saw the discussion of Dale and Don about the search order
(fillpattern) for rubiks tangle come by, and wondered why they both
missed an even better search order (the best?):

Don:             Dale:            Jan:              Equivalent to:
 1  3  5  7  9    1  2  6 10 15    1  2  5 10 17    17 16 15 14 13
 2  4  6  8 10    3  4  7 11 16    3  4  6 11 18    18  5  4  3 12
11 12 13 14 15    5  8 12 17 20    7  8  9 12 19    19  6  1  2 11
16 17 18 19 20    9 13 18 21 23   13 14 15 16 20    20  7  8  9 10
21 22 23 24 25   14 19 22 24 25   21 22 23 24 25    21 22 23 24 25

I missed it on the 5x5 because my program was fast enough that I didn't
look further. When I modified my program to try the 10x10 last week, I
did come up with the ordering Jan suggests. It shaved about 1/3 the
running time off my 5x5 search, but it actually doesn't seem to make
that big a difference in the 10x10.

It turns out the 10x10 search isn't quite as bad as I thought, because
the tree does get trimmed rather early. When a piece is constrained on
two edges, there are on average only 2/3 choices for that piece. I've
got my program chugging along, and so far it has eliminated 4 of the 96
choices for piece (w/ orientation) for the upper left corner. There are
4896 choices for the first 4 points in the search order, and it's going
through one choice per 25 minutes on average, so it'll finish in a mere
3 months, if I have the patience for it. (I may try to dig up some
otherwise idle workstations to leave running over the holiday break.)

-- Don.