Is this board solvable?

Can anyone tell me an answer to this Minesweeper problem. I have to find just 2 mines from 4 spaces. What I really want to know is the sure shot way to solve puzzle (no guessing)

I have found all but 2 mines in lower right corner position.

I want an explanation to the answer. I am not obsessed with Minesweeper, but with the solution. Also if answer involves some mathematics, I will try to understand that.

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4 Answers

The board isn't solvable, since there are multiple valid solutions.

Assuming you're playing the Windows Phone version of the game, there are various power ups which you can use to reveal where the final two mines are.

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Yeah, but I am using the ones which finalizes all flagged position against possible mines. Bad choice here :D – Master Chief Jan 31 '13 at 15:21
That 2nd one was the answer. My brother used all his luck for the day to uncover those :D – Master Chief Feb 2 '13 at 4:50

The original problem

``````X31
X??
X4?
12?
``````

Possible answers:

``````X31    X31    X31    X31
X4X    X5X    XX2    XX1
X42    X4X    X4X    X42
12X    121    121    12X
``````

Each of the tiles have equal probability of being a mine (50/50).

There is a wrong move, which is to try the corner or the tile next to the corner. If you try those lower tiles, you do not reveal enough information to avoid a second guess (odds of winning = 1/4). If you try either of the two higher tiles and win, there will be no second guess (odds of winning = 1/2).

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This situation actually happens fairly frequently in Minesweeper. It's a bit of a flaw in the puzzle, if you expected it to behave in a manner that can be solved using reasoning only. – Kenogu Labz Jan 31 '13 at 23:41
I'm confused on how the odds of winning this are 50/50 if you choose one of the upper tiles. Can you explain please? – mowwwalker Feb 2 '13 at 3:59
If you choose an upper tile, either you lose, or you don't. If you didn't lose, you'll know whether the tile next to the corner is a mine or not, so you won't have to guess about the corner or its neighbor. You can see this in the answer because the upper tiles change values based on the position of the lower tile mine. – David B Feb 2 '13 at 4:51

There is no one possible solution for this puzzle. It's a matter of luck now.

Every box is a possibility for every number.

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Now that is bad – Master Chief Jan 31 '13 at 15:14
No! This! Is! Minesweeper! – Task Jan 31 '13 at 15:15
It is not just luck, there are still 2 locations where you should not gamble for. Keep thinking. – Dorus Jan 31 '13 at 20:05
That is nonsense. There is no way to solve that position applying logic, without any gambling. There are two completely independent ways of satisfying the 3 and the 2, and both of them satisfy the 4. – Kaz Jan 31 '13 at 22:01

Yes, it is solvable without guessing. First, you can reduce the 3 to a 1, the 4 to a 2, and the 2 to a 1 making the board look like this.

• 11
• XX
• 2X
• 1X

Then, you can further reduce the two to a one because you know that one of the mines have to be on the upper side. After that, you basically got an 1-1 situation at the bottom. Then your board will look like either one of these:

• 11 ----------- 11
• X1 ----------- X2
• 2X ----------- 2X
• 1X ----------- 1X

Depending of which one of these two, you can find out the answer without guessing

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How did you - without guessing - determine that the upper-right unknown couldn't be a mine? – Michael Madsen Nov 27 '13 at 8:53