Mines are most quickly found when a situation I call "complete determinism" occurs. There are only a few of these situations that occur when an auto clear happens in a game, and learning to spot these situations quickly is the first step to better Minesweeper times. These situations will be described in detail. Complete determinism also occurs when additional cells have been cleared, and it takes practice to see these situations quickly.

One on the Corner
Sometimes when an area auto clears, there will be "corners" that appear which have a blue "1" diagonal from them. See Figure 6(a) for an example. These corners scream, "I have a mine here!" Figure 6(b) highlights the corner blue "1" and its neighborhood of eight squares.

In the neighborhood around the "1", seven of the eight squares (all but one!) were auto cleared by Minesweeper. Therefore, the one remaining covered square must have mine in it! There is no guessing to be done, just flag the square containing the mine.

Figure 6
(a) A blue "1" at a corner. Learn to spot these quickly. (b) The pink area highlights the neighborhood of the blue "1". Only one cell is covered, so it must contain a mine. (c) The mine is flagged.

Since there is no guessing involved with finding the mine next to this particular blue "1", it is a "completely determined" situation.

Two at the Edge
Another completely determined situation occurs when a green "2" appears at the edge of the minefield, against a line of covered squares. But we must pause for a moment here to expand upon the meaning of the number appearing in the minefield.

All numbers describe the number of mines hidden in the squares surrounding that cell. For cells in the middle of the board, there are eight neighbors. But for cells at the very edge of the minefield, there are only five neighbors. And for the four cells in the corners, there are only three neighbors.

Figure 7 displays the situation I call "two at the edge". Here the green "2" at the edge of the board has had all but two of its neighbors auto cleared by Minesweeper. Therefore these two squares must contain mines.

Figure 7
(a) A green "2" at the edge of the minefield. (b) The pink area highlights the five neighbors around the green "2". Two cells are covered, so they must both be mines. (c) The mines are flagged.

Three on a Wall
The last common example of complete determinism that occurs when an area auto clears is what I call "three on a wall". When a red "3" appears against a line of uncovered cells, the three remaining cells all have mines underneath them. Figure 8 displays this situation.

Figure 8
(a) A red "3" against a wall of cells. (b) The pink area highlights the eight neighbors around the red "3". Three cells are covered, so they all must contain mines. (c) The mines are flagged.

As you may have noticed, there are actually two "3"s that occur on the wall in the example in Figure 8. The lower "3" can be flagged in a similar fashion.

Other Examples
Figure 9 presents some additional examples of complete determinism, which occur after one click. They don't happen very often, but they are presented here to help expand on the idea, and to help you "see" how a number describes its neighbors.

Figure 9
These are two more examples of complete determinism.

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