# Minesweeper mental exercise

#### Jake Bunce

##### XenForo moderator
Staff member
I realized I haven't done one of my minesweeper threads on this forum yet. Minesweeper is one of my favorite games. It is much more mentally engaging than most people allow it to be. Lots of proof by contradiction in otherwise "guess" situations.

Prove that the yellow square has a mine.

#### CTXMedia

##### Formerly CyclingTribe
You can't - the numbers don't stack up - there's more than 1 possible mine for all the surrounding plots so it could be either the yellow square or the one to the right of it!

#### Jake Bunce

##### XenForo moderator
Staff member
You can't
You can. There is a proof for this situation. I will post it if no one gets it.

#### RobParker

##### Well-known member
Does a red flag mean you've correctly identified a mine or just guessed? It's been years since I played it.

The answer looks like it revolves around the two 3's on the right but not sure what the flags mean

#### Slavik

##### XenForo moderator
Staff member
The yellow one has a mine in it because if the one next to it has a mine it means the 2 left MUST have mines to satisfy the 4.

This means the 2 (3 left and 1 up from the yellow) eliminates too many boxes around it for the 4 (4 left and 1 up from the yellow) no longer has enough available boxes around it to satisfy the 4 mine requirement.

In short, if the yellow box DOESNT have a mine in it, the 4 square which is 4 left and 1 up from the yellow box doesn't have enough boxes around it to satisfy the 4 mine requirement because the 2 box next to it eliminates too many boxes.

Slavik is right.

##### Well-known member

The red dots are the ones that would have to be mines if the yellow square wasn't a mine. The 4, like Slavik said, would not have enough mines next to it because of the 2 that is next to it.

#### Chris D

##### XenForo developer
Staff member
Hmm, found this quite easy...

I started by adding the mine next to the 3 (highlighted in yellow).

That has to have a mine due to the position of the 3 to its bottom left.

ARGH... just noticed a mistake... technically there could be a mine in the space I've crossed out. So actually this solution isn't as easy as I thought.

****.

#### Jake Bunce

##### XenForo moderator
Staff member
Slavik wins. Sador's illustration is correct.

#### CTXMedia

##### Formerly CyclingTribe
lol ... that's probably why I was never any good at it.