Is this board solvable?

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.

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).

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

Every box is a possibility for every number.