Creating sudoku initial boards

Question

Is there an algorithm or way I can get initial state sudoku puzzles for a sudoku game. Preferably with the ability to have different levels of difficulty?

Answer 1

Basically there are two approaches. In both you need to have 2 solvers, a humanlike solver, which uses strategies performable by a human and a backtracking solver.

With the first approach you generate a random complete solution and iteratively remove random cells solutions. Backtracking solver will make sure, that there still exist only one solution, while the human-like solver will make sure, that its still solvable by human and it can be also used to measure the difficulty of the puzzle.

The second approach works in an opposite fashion. Firstly you create an empty board and place there randomly 17 cell solutions (in a consistent manner). 17 is the lowest filled cell count known to genrate a puzzle with unique solution. Now the algorithm in every step checks, if it has already an unique solution and if not, it adds another (consitently) filled cell. If the solution guarantees solution uniquesness and the puzzle is solvable by a human and the difficulty is below some limit, than the algorithm terminates.