tarek wrote:It turns out that The backdoor size 3 under the FN constraints does not correlate with difficulty as we would have hoped....

would that still be the case with a backdoor size 2-3 but with the complete arsenal of constraints (forgive me gsf, I lost track of the constraints in your solver)

the known M3 (singles backdoor size 3) puzzles all have FNB (singles+box-line/locked-candidates) backdoor size 2

except the Easter Monster which has FNBT2 (singles+box-line/locked-candidates+naked-pairs) backdoor size 2

so it doesn't take much more technique strength to weaken the backdoors

The reason why I'm suggesting this is that techniques following FN are not always difficult. but A BACKDOOR SIZE 2 UNDER Sudocue techniques for instance, can correlate with extreme difficulty.

with the kitchen sink all puzzles in the

q1 taxonomy catalog (this includes the hardest from the player's forum) have backdoor size 1 or 0

the q1 taxonomy has a range of q1 ratings from 1 through 99408 (JPF's Easter Monster)

q1>3000 requires guessing in my solver, but there are lower ones that do so also, e.g. q1==71

I had hoped that the q1 ratings for puzzles not requiring guessing would provide insight

into the constraints that solve the puzzles, but that doesn't seem to be the case

my solver doesn't do uniqueness/als constraints -- maybe that skews the observation

recall the the q1 rating uses naked/hidden singles (and box/line for the very hardest) in singleton and pairwise propositions to rate puzzles