finally got some time to respond
I collated recent puzzles and added them to
q1-taxonomy-2007-11-11.dat -- thanks
the high suexrat9 ratings are a neat achievement
suexrat9 is based on a backtracking solver that uses singles to propagate constraints
the rating counts nodes visited during the backtrack search
its DLX based, so the node count will be much higher than some non-DLX based solvers (like mine)
it washes the inherent bias in the basically deterministic search algorithm
(it uses the time honored search strategy of asserting the most constrained variables first)
by running the node count search multiple times on pseudo random permutations of the input puzzle
the -q1 rating is also based on singles (but has a fallback to add locked candidates for the hardest of the hardest puzzles)
it differs from suexrat9 in that it makes all propositions, in order of tuple degree
(e.g. bivalue first, then trivalue etc., stopping after the lowest degree that advances the solution),
rather than a random sample
the hardest puzzles require multiple rounds of nested propositions, with small numbers
of placements/eliminations for each round of propositions
I believe that the aesthetic rating we are aiming at is related to the statistics gathered by
the P constraint method used by -q1
the ratings output by my solver are basically polynomial functions of the counters accumulated
by the constraint methods applied
that function can be tweaked with the -R option to meet our collective ideas of hardness
running -v2 -q1 on the golden nugget shows that it is in a class by itself in the q1 taxonomy
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propositions 137484 solutions 4 contradictions 0 iterations 334982 girth 22 degree 5 nesting 2
it only yields to nested propositions
out of 100K of them only 4 provided placements/eliminations that advance the solution
in this case it was 4 actual solution paths
degree 5 means that bivalue 3-value .. 4-value propositions produces no info
only 5-value/5-location cells did, and only 4 pairs at that
girth 22 means that some of the singles propagations after propositions required 22 iterations
to reach steady state
girth is roughly analgous to chain/cycle length
the -v2 numbers above correspond to the P portion of the Q1stats field in q1-taxonomy.dat
for the golden nugget its
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P1.2.137135.4.0.334061.22.5.2.236
for comparison easter monster required 9 rounds of 400K total propositions at degree 5 girth 25
using singles and locked candidates (V3 in the Q1stats field)
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P9.16.467645.2.20.1697341.25.5.2.238
maybe the librarians/collators among us can pick out the puzzles that seem out of whack among the different ratings
then we can look at the P stats to see if they provide enough info to make sense out of the discrepancy
I'm not saying that the answer must be in the P constraint counts
just that its in a form that can be experimented
Taking up RW's remark, I generated 101 puzzles with this pattern imposing what I still think of as the 'dml' rule, that all values are distinct in each band and stack. Of these, only one was not mimimal. The SE rating and frequency of the others are given in the table below (ignore the Index column).
