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It should be fairly obvious that it is impossible to solve a minesweeper game without at least one guess, but beyond that, is there any way to characterize sufficient and necessary conditions to then win a minesweeper game with subsequent perfect play?

In fact, I am more interested in figuring out what are the necessary conditions to arrive at a win in minesweeper.

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1 Answer

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Decision version of Minesweeper is NP-complete, because it is possible to encode logic gates on the minefield (reference). So one should not expect any nice criteria that determine solvability of a given field.

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