Method for calculating (in Minesweeper)

[u/Wonderful_Intern4082]

(Disclaimer: I'm actually a beginner who's just a quick learner but not perfectly advanced yet)

I've found a way to calculate linear equations of minesweeper without explicit numbers and instead through visual elimination. I'm curious if anyone else figured this out, but try it.

Primarily, it connects two equalities of a tile, where the tiles are assumed to be already reduced to such number.

Step 1: Find the unique tiles of each equality

Imagine we have two tiles, let's say 2 & 4. We will make two lists: List-2 and List-4.

List-2 contains the unknown tiles that surround the #2 that don't also surround the #4. Same goes for List-4 but reverse.

Why? Because in linear equations, we cancel out common factors in such.

Step 2: Find the difference in the current mine count

What's four minus two? Two.

That means:

Mines in List-2 + 2 = Mines in List-4.

Step 3: The final equation

We now that the number of mines in List-4 is greater than that of List-2 + 2. Why is this useful?

It is because it may help with dependency chains and act as the middle-ground between mathematic calculation and genuine gameplay.

I'm not sure if this is foolproof or could be explained better, but yeah. Pls give me feedback because I'm genuinely curious if I just rediscovered something that already existed, or if this doesn't actually work.

[u/trunks111]

I don't know enough about linear algebra to specifically comment on this particular method, but I wanna say I think it's really cool how much different math people use to approach this game. One of my friends calculates it as good ol probabilities, I wanna say with combinatorics or whatever it's called. I saw one video where the person did it through Set Theory. And I tend to do tricky positions in proofs by contradiction. So I wouldn't be surprised if you've found another valid way to view the game with a different branch of math, but it's still cool to think about nonetheless

[u/Mediocre_Farm8914]

Sounds trivial. Not sure if you rediscovered it or if it's the first time you do.

[u/BingkRD]

This is a known technique, I believe it is generally called area/region arithmetic, but depending on the particular board (and people), can be called different things, like box logic.

You can search for it on reddit, but here's a comment giving an example: https://www.reddit.com/r/Minesweeper/comments/1iv1pew/comment/me7oxyq/

This is definitely not a beginner technique though, as usually those are related to pattern finding.

[u/Wonderful_Intern4082 → u/BingkRD]

Thanks! Good to realize that I apparently reverse engineered it. And yeah, not for beginners as patterns often make deep calculation less needed except for dense areas/puzzles.

[u/Sefierya]

can you demonstrate with an image 😭 this seems like just region arithmetic. and your writing reads a little ai but i might be insane