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

- Code: Select all
`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

- Code: Select all
`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)

- Code: Select all
`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