[maggit]

It's been some years, but I think it boils down to the definition of when you are _considering_ some part of the game state.

Right off the bat, I cannot agree that abc must contain exactly 2 mines. From what we can see, abc contains _at most_ 2 mines. There may or may not be mines in what you have left out, and we cannot know without considering what's there.

I haven't written a formal proof for that statement, but I have been unable to solve it to my own satisfaction by reasoning about a reduced view of the board.

[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.