because brute-force executes very quickly for easy sudoku's but as it gets harder and lesser values are provided it takes too much time.

I have a suduko solver. It is what I consider "brute force", though it does not look any further down boards that do not satisfy the constraints of the game (i.e. values unique in rows, columns, 9-cells). Typically it executes in < 0.5 seconds. Can you supply a "hard" puzzle that will take too much time?

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...