Depending on how experienced you are with minesweeper, this situation may not seem very difficult. It gave me a little pause, though. In the process of making this game, I have played it many times, but it’s interesting moments like this one that keep the game from being monotonous. Sudoku is ultimately a better pure logic game, in that it can provide a consistent level of difficulty. The random setup of a minesweeper-type game, by contrast, means that more interesting situations arise haphazardly (indeed, solvability is not assured), though adjusting the number of mines is a crude lever for changing the difficulty. The answer to whether or not there is a solution in this situation is after the break.

This configuration is solvable. Suppose that, of the six blocks still to be determined, the lower left one sandwiched between the two tiles with value 2 has a mine (see picture). Then the circled tile with value 1 on the left is covered, implying there are no mines in the exed out tiles. However, this contradicts the tile with value 1 on the right, so that there cannot be a mine placed in that spot.

By a similar argument, it is impossible for there to be a mine in the lower right position (above the tile saying “dude!”). Thus, since there must a mine in one of those three lower tiles, it must be in the middle position. After revealing the left and right tiles, one can easily determine the safety of the remaining tiles.

Update 6/26/08:

Nic sends me a screen shot of a truly unsolvable puzzle (as far as I can tell).

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