## Difficult Sudokus Created by Replica Exchange Monte Carlo

### Difficult Sudokus Created by Replica Exchange Monte Carlo

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.)
dobrichev
2016 Supporter

Posts: 1830
Joined: 24 May 2010

### Re: Difficult Sudokus Created by Replica Exchange Monte Carl

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
JPF
2017 Supporter

Posts: 5939
Joined: 06 December 2005
Location: Paris, France

### Re: Difficult Sudokus Created by Replica Exchange Monte Carl

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
Leren

Posts: 4345
Joined: 03 June 2012