This program can solve and generate standard 9 by 9 Sudoku's with a simple GUI.
This uses a standard randomised backtracking algorithm to solve the Sudoku, and returns that the given Sudoku is unsolvable if no solution is found after searching all possible arrangements.
To generate a new Sudoku grid, this program solves the empty grid: because the solving algorithm is randomised, this generates a randomised solution. Then, the algorithm randomly empties tiles to generate an incomplete grid.
You can change the difficulty of the generated Sudoku's by changing the value of NUM_GENERATE in Gameboard.java. This is the number of tiles which are generated.