Do you know of any formula to calculate the difficulty score of Sudoku?

Question

I am looking for a formula to measure the difficulty level of a Sudoku solution.

Answer 1

In Pelánek (2011)¹, Sudoku difficulty evaluation was investigated across four existing metrics. These are based on incidences of various logic techniques (see constant folding). Results based on Spearman's correlation coefficient are given in Table 1.

Evaluation of difficulty through dynamical systems has also been explored². In this setting, one considers the association between the difficulty of a Sudoku puzzle and the system's chaotic behaviour. The result is obtained by solving a coupled system of two differential equations after converting the Sudoku satisfiability problem into conjunctive normal form.

_References

_{[1] Pelánek, R. (2011). Difficulty rating of sudoku puzzles by a computational model. In Twenty-Fourth International FLAIRS Conference.}

_{[2] Ercsey-Ravasz, M., Toroczkai, Z. (2012). The Chaos Within Sudoku. Scientific reports. 2(1):1-8.}