May create sudoku boards with multiple solutions

[Gennadiyev]

For a sudoku board to be valid, there should be exactly ONE solution to an unsolved board. That means the difficulty parameter (in float) could tamper the legitimacy of a sudoku problem.

There are quite a lot of solutions for creating sudoku boards with only one solution.

[alexisflesch]

I think a better way to create puzzles would be to start with a full grid, but instead of randomly removing a certain amount of cells, randomly remove cells one by one until the puzzle is no more uniquely solvable. Then, we could remove between 0 and 100% of the unnecessary cells.

I just made a pull request with a way of knowing whether a grid has a unique solution or not. If someone wants to go forward from this, it should not be too hard.

By the way, thanks a lot @jeffsieu for your work, it gave me a nice way to generate pdfs of Sudokus of various sizes and difficulty !

[ChronoDK]

How do I force it to generate a sudoku with only one solution? With the latest version I can check for multiple solutions, but how can I make it not generate those bad boards at all?

[alexisflesch]

The algorithm used to create boards goes as follow:

1. Create a valid board
2. Randomly remove some percentage of the values

So the short answer is : you can't. What you can do though is to use a quick and dirty approach:

1. Create a valid board
2. Check whether it has a unique solution:
   • if not, go back to 1.
   • otherwise you're good to go.

What should be done is to write a function that goes like this:

1. Create a valid board
2. Remove (randomly) values one by one until the board is no more uniquely solvable (try every remaining value to be sure that it is as empty as can be)
3. Remove some percentage of the values found in step 2 to create a uniquely solvable grid with given difficulty.

[ChronoDK]

Thanks, I did the quick and dirty. It's fine for now.