# What is the next move on this minesweeper board?

Here is the board

I found an online minesweeper solver which can deduce what the next move is, so I know what the next move is and that it is logically obtainable. But it doesn't offer much help in explaining it, so I can't really learn from it.

So a solution here needs to provide a correct explanation.

• Keep in mind that unlike other classic grid-deduction puzzles, Minesweeper always has an element of luck to it, given there is hidden information. So while there is a logical next move in this case (as several answers have pointed out), that is by no means a guarantee. Mar 23, 2022 at 13:57
• The version of Minesweeper I am playing guarantees there is always a logical solution: chiark.greenend.org.uk/~sgtatham/puzzles/js/mines.html Mar 23, 2022 at 16:29
• @ChechyLevas That's helpful to know. Sometimes knowing there is a solution is the clue that gives you the solution. Mar 23, 2022 at 20:57

Consider the section at the bottom-centre of the grid:

Exactly one of the two cells marked here with blue squares must be a mine, to satisfy the blue '1' clue to their left. This same mine will also satisfy the blue '1' clue to their right, so all other cells adjacent to that blue '1' must be safe (indicated here in yellow):

Similarly, exactly one of the two cells marked here with green squares must be a mine, to satisfy the green '2' clue between them (and the one to its left), which already has one of its two mines known. With this in mind, since we know two of the other three cells that are adjacent to the rightmost green '2' clue in this area are safe (shaded yellow), the cell beneath these on the bottom row must be a mine as it is the only space remaining that can account for its second mine.

This then has immediate knock-on deductions for the cells marked with green and blue squares. Hopefully you should be able to make further progress from there...

• It's so obvious when you point it out! Mar 23, 2022 at 8:13

When I see this situation I don't even need to think.

When you have the pattern 1-2-1, regardless of what other cells are uncovered, or whether there is a wall, the green cells are safe.
This is one of the useful tricks to know, this pattern being quite common.

• This is very interesting. Unlike the other answers which are specific the use-case, this is a very nice general rule which is relevant to the OP's question. (I would only add that it works horizontally too, obviously). Mar 25, 2022 at 12:28

I feel like my answer is a slightly different way of looking at it :

We're gonna try to guess if the yellow square contains a mine or not. Let's suppose that it does and we'll see that we reach a contradiction.

Because of the two 2's that are above the yellow square, and because of the circled 1, we can say that the 3 crossed squares do not contain a mine.
This means that the blue square must contain one to satisfy the 2 adjacent to it.
The green square also has to contain a mine because of the 2 adjacent to it.

We thus get to a contradiction : the blue and green square can't both contain a mine because of the 1 that's inbetween them. Thus the yellow square cannot possibly be a mine ! From there you get pretty much to the same point as Stiv.

• I don't understand why the three crossed squares can't have a mine. It could be in the NW one (relative to the rightmost 2), which would satisfy the other two 2s, and the circled 1 would be satisfied with a mine in the E or SE squares. Mar 23, 2022 at 12:24
• It can't be the NW one, because then the 2 above the yellow square would have to be a 3. Mar 23, 2022 at 12:29
• @Simone perhaps you've missed the bit of text above the picture : we're working under the assumption that there is a mine in the yellow square ! then, we show that we reach an impossible situation. Mar 23, 2022 at 12:56
• @GabrielH that's exactly it - my fault, I missed that. ChechyLevas, good approach. Mar 23, 2022 at 13:14

Due to the center bottom-most 1 there is one mine in three blue squares.
Then, due to the 2 above it, there is one mine in one of the two pink squares.
Then, due to the 1 above it, there is no mine in any of the three green squares, and in the dark blue one, either.

Once the green squares get cleared, it'll become obvious the 'pink' mine is on the left, consequently the 'blue' one is on the right.

Result:

Black dots are empty squares, but we don't know what numbers will appear there.

• @Auribouros Thank you for the edit. :) Mar 23, 2022 at 13:22

Well, I would continue with revealing the field as marked in the following:

(It cannot hold a mine since either the field two steps left or the one two steps left one step up must hold one because of the 1 three steps left.)
That way you get to know whether the field two steps below holds a mine or not. The field one step below cannot hold a mine as this would result in a contradict with the nearby 1s together with the 2 left to it.