What algorithm creates tasks in this game?

Question

Image processing

There are several similar games in Google Play, one of them is free:
https://play.google.com/store/apps/details?id=com....
There are also in iTunes, I don’t remember about free ones.
The essence of the game is to paint over the playing field with your finger, drawing paths (path) from colored cells with numbers to other cells with the same color and number so that the length of the path is equal to the numbers at the ends. Everything is simple.

The question is how to ensure the uniqueness of the solution to the puzzle, that is, so that the paths are known to be predetermined?

Answer 1

What does not fit the decision on the forehead?

Answer 2

I would think in the direction of the algorithm from the reverse - first place some completed very simple task, and then change it with a series of manipulations (remember the tags). So you will definitely get a solution to the problem. The number of permutations (and their algorithm) will determine the uniqueness of the resulting task.