This is, what it looks like now. But the last word is not spoken. Not long time ago it seemed, that only puzzles with diagonal pattern could make it.tarek wrote:My theory of 21-clue puzzles not having the hardest puzzles was rubbish...

Thanks again.Did I forget ravel to mention how splendid your work with these hardest puzzles is

The program is in progress. So far i have no new techniques implemented, but one less (UR1) But i want to add xy-wing, UR1,2,4 and turbot fish (and i am rather curious, what they will bring). New are the subnets and the way, how i calculate solutions.could you elaborate on how your new method works .... (what new techniques are implemented, and when subnets are used)........

For this i keep a list of "nodes", that are the grids, where the implemented techniques are stuck, with rating so far (one point for each elimination chain needed, 3 extra points for elimination that needs subnets). For "the next" node (in the moment by order of lowest ratings) i calculate, which eliminations are possible by trying all wrong candidates. When a number leads to a contradiction and the elimination of the number in the original grid would lead to at least k (k is set to 2 now) more eliminations using the basic techniques, this grid is added to the nodes with rating + 1. Here i keep a list that holds the minimum number of "allowed" candidates for each rating number (this is now the second best number found so far). Only grids with less or equal candidates are added. Also i check for duplicates, because often eliminations lead to the same grid.

If no such elimination could be found, i am looking for subnets, the most time consuming part. This is done the same way (again keeping a list of nodes), but i give up, whenever no direct elimination with enough progress can be found, and i stop with the first subnet, that leads to a contradiction. The grids resulting from subnet eliminations then also are added to the nodes with the extra points, if good enough.

The process is continued, until no better solution can be found from the nodes (none is left with less equal than the minimum number of candidates for the rating level).

So this rating now should be the same for all equivalent puzzles also.

Much can be improved, mainly the speed (needs about the same time as calculating the ER now) and - as mentioned - more techniques.

But i will need holidays from Sudoku now to have enough time for "real life" again (my friend says, there are also other things of worth out there)