When the brute-force method is a simple algorithm and executes very quickly, why bother using other methods?
A legal puzzle must have only one valid solution.
Update: I googled for a hard sudoku board, got http://www.forbeginners.info/sudoku-puzzles/hard-1.htm It was brute-forced in 0.038 seconds on my laptop. Code is here: http://github.com/AnthonySteele/SudokuSolver/commit/b953ef97...