Here is probably the breakthrough of the year in Sudoku.
THE FOLLOWING TWO PUZZLES FOUND BY MITH ARE NOT IN T&E(2):
- Code: Select all
........1.....2.......3..45..6.......71.8....23..67..8.827..1..6...23...7.381.6.. ED=11.9/1.2/1.2
........1.....2.......3..45..1.23....267.81..73.61.8...17.6.....8.......2.3.87..6 ED=11.8/1.2/1.2
Mith, all my congratulations for this exceptional finding.
First consequence: my very old T&E(2) conjecture (~2008) no longer holds. Notice that exceptions to it can only be extremely rare, knowing that puzzles not in T&E(1) are already extremely rare - of the order of 1 in 30M.
Second consequence: this opens a totally new approach to the search for the really hardest puzzles.
Instead of searching for high SER, search for puzzles not in T&E(2). This implies trying billions or trillions of puzzles but very fast generators already exist and a very fast T&E(2) procedure can be written (contrary to the SER test).
The only disadvantage of this approach would be it can't produce any of the already known 'hardest" (except the above two).
One clear advantage is, my T&E(n) classification is intrinsic and stable under Sudoku isomorphisms.
Note1: the existence of Sukakus not in T&E(2) and not derived from sudokus was already known.
Note2: the other 11.8s in the last batch (28 Feb.) are in T&E(2).