Minesweeper has been shown to be NP-complete [1]. So if there's a way to avoid "brute force" and guarantee a polynomial-time solution to an arbitrary board, that would be a proof of P=NP and win you a million dollars, worldwide fame (at least among theoretical computer scientists), and a citation of that work in theory of computation textbooks for a long time to come.

[1] http://web.mat.bham.ac.uk/R.W.Kaye/minesw/ordmsw.htm