  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.)
