I am glad to see a topic about minimal givens on Sudokus, but I think that minimum givens on n*n Latin Squares is more natural and mathematical. For any size n there is a puzzle with floor(n^2/4) givens(OEIS A002620), with every number going diagonally and givens in two triangles, And that number of givens has been conjectured to be minimal. We have not found any helpful public research on the Internet.

I have something to share about this problem and some patterns in Latin Squares. And you are welcome to discuss with us if you are interested or you spot some useful articles, or you have your own view.