Yeah, it's NP-complete to decide whether a cell in Minesweeper must be a mine: https://logic.pku.edu.cn/ann_attachments/np.pdf.

In practice I suspect a SAT solver would make quick work of the positions that actually appear in games.

There was a Minesweeper on here that used a SAT solver, but I cannot find it at the moment. As I recall, it never had any issue with resolving the board quickly. I think it dynamically resolved where the mines would be as you played the game, and if you clicked a square that could be a mine, it would be a mine, except, I believe, when there were no open squares that were safe.

(Edit: Here it is! https://pwmarcz.pl/kaboom/ And the write-up: https://pwmarcz.pl/blog/kaboom/ )

This is similar in spirit to my take on the game: https://magnushoff.com/articles/minesweeper/

Unfortunately, not being familiar with SAT solvers, my implementation can grind to a halt in some configurations :)

I wonder if one learned to play faster with this kind of minesweeper.

I find in a lot of repetitive learning, you have a very noisy signal, you don't know if you succeeded because of luck or you did something right.

This variant takes out the luck part.

I made winsweeper, which will move the mine if there is no safe tile left for you to discover.

https://github.com/alaingilbert/winsweeper

Yeah I've debugged another game that attempted this and this system resulted in the game lagging as hard sometimes.