[StevenWaterman]

Sorry, I left out some bits of the game state for conciseness - perhaps this is a better way of displaying it

    .---       a---
    .2--       bX--
    .22-  as   cYZ-
    ....       defg

Where:

. means unknown

- means clear (and in a real game would reveal a number and therefore a constraint, but we don't need to consider those numbers for this solution)

a number means clear and producing a constraint that we want to use

This mirrors the game state in the article, and would allow us to assert that abc contains exactly 2 mines, while still only having to consider a 4x4 section of the board.

Thanks for helping me with this btw, it's much appreciated :)

[maggit]

Right, so, in my book, reasoning based on facts such as "these squares are clear" are _considering_ those squares.

This is in contrast to the local rules I first describe that consider only a very limited part of the board, and there is a pre-determined hard limit for how much would ever need to be considered for these rules.