I'm trying to make a Sudoku puzzle generator. It's a lot harder than I expected and the more I get into it, the harder it gets! My current approach is to split the problem into 2 steps: Generate a complete (solved) Sudoku puzzle. Remove numbers until it's solveable and has only 1 solution. In step 1, since I'm using a brute force methods, I'm facing some run time issues. Is there an optimal way of filling in a complete Sudoku puzzle? In step 2, what kind of algorithm should I use to "puzzlize" a solved sudoku?