coloin wrote:A newer method ?

A new method based on old discoveries.

Read

this eleven's post which is referencing

RW.

So, what I did took 30 minutes coding, 1 second execution, and several hours verification.

1) get a valid puzzle.

2) find its unique solution.

3) create a complementary puzzle by reverting the givens, i.e. in the solution grid erase all givens and leave all non-givens.

4) solve the complementary puzzle and store all solutions.

5) for each solution replace the given values in the original puzzle with the respective values from the solution.

6) repeat for all known puzzles in the family.

7) remove duplicates.

In other words, find the puzzles isomorphic to the existing ones by permuting the values in the unavoidable sets which lie entirely in the puzzle givens.

Reconsidering the "essentially different puzzle" definition would cut off 69 of the first 82 39s + all mines, resulting in only 13 "different" 39s.

For 17s collection there are 96 isomorphs in this sense, all in the Gordon's list. Seems this processing has been done before (and therefore this is not a new method). It took 10 seconds.

Nevertheless this check will speed up the new 39s discovering process - at least by enlarging (or truncating) the seed collections of 37s and 38s.

I kept eleven's collection of 38s published just before the old forum crash. It has 31348 38s. A pass checking for UA isomorphs found 11054 "new" puzzles (320"), and 16286 isomorphs within existing 38s.

MD