The New Sudoku Players' Forum

[dobrichev]

Difficult Sudoku Puzzles Created by Replica Exchange Monte Carlo Method from 2013, by Hiroshi Watanabe.

An algorithm to create difficult Sudoku puzzles is proposed. An Ising spin-glass like Hamiltonian describing difficulty of puzzles is defined, and difficult puzzles are created by minimizing the energy of the Hamiltonian. We adopt the replica exchange Monte Carlo method with simultaneous temperature adjustments to search lower energy states efficiently, and we succeed in creating a puzzle which is the world hardest ever created in our definition, to our best knowledge. (Added on Mar. 11, the created puzzle can be solved easily by hand. Our definition of the difficulty is inappropriate.)

[JPF]

Here is the puzzle found, "minimizing the energy defined by the Hamiltonian":

Code: Select all

 . 6 1 | . . 7 | . . 3
 . 9 2 | . . 3 | . . .
 . . . | . . . | . . .
-------+-------+-------
 . . 8 | 5 3 . | . . .
 . . . | . . . | 5 . 4
 5 . . | . . 8 | . . .
-------+-------+-------
 . 4 . | . . . | . . 1
 . . . | 1 6 . | 8 . .
 6 . . | . . . | . . .


not really difficult and even not minimal...

JPF

[Leren]

Here is the puzzle in line format : .61..7..3.92..3..............853..........5.45....8....4......1...16.8..6........

Tough puzzle, solved in singles. Hodoku agrees.

Leren