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Related: Is this board solvable?

The following happened playing Minesweeper:

Minesweeper screenshot

As far as I know, there was no way to know for sure where the remaining two mines are located.

How does one correctly determine whether the Minesweeper board is no longer solvable?

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Firstly: Note that both mines can't be in the top two spaces - i.e. there must be a mine here:

enter image description here

From that you can see there can't be a mine in the middle space - so the two mines must be at the top and the bottom of the column of three and not in the middle.

In terms of whether it is solvable or not: the only real way to tell is if the puzzle has multiple solutions - i.e. you can place the mines such that the conditions of the puzzle are satisfied in more than one way. In this case, the only possible solution is the one described.

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  • They turned out to be in the upper and bottom tile. According to your post this should've been foreseen?
    – Mast
    Apr 25, 2015 at 14:11
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    @Mast Yes. The "4" square already has 3 mines adjacent to it.You can see that the two remaining mines can't be in the top two spaces, otherwise the "4" square would have 5 mines adjacent to it. The solution then follows from this information.
    – imulsion
    Apr 25, 2015 at 14:13
  • Great. Now I know this board was solvable, but the original question still stands.
    – Mast
    Apr 25, 2015 at 14:14
  • @Mast Edited the answer
    – imulsion
    Apr 25, 2015 at 14:16
  • It's not quite right to say that it is unsolvable if you can place the mines in multiple ways, because right after your first click you have many different mine placements that are both valid and consistent. Instead, a game is unsolvable if there is no square for which you can be certain that it does (not) contain a mine. You can check this (inefficiently) by trying out all valid combinations of mines and then seeing if there is a square that does (not) have a mine in all of these combinations.
    – FWDekker
    Aug 6, 2020 at 22:41

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