There are some number combinations that occur which always result in the same pattern of mines. These situations can be solved using partial determinism, but play much faster if you just recognize them and mark them accordingly.

The One-Two-One
When a "2" occurs on a wall with "1"s on either side, forming a "1 2 1" combination, the mines are always adjacent to the "1"s. I usually proceed by clearing the cell adjacent to the "2", and then flag the cells adjacent to the "1"s. Figure 15 outlines the situation and the procedure.

Figure 15
(a) A "1 2 1" situation. (b) The "2" is highlighted with its three covered neighbors. (c) The cell next to the "2" can be safely cleared, and its remaining neighbors flagged.

You may proceed in whatever way is quickest and easiest for you, but I find it easier if I "split the two" and flag the remaining two cells, which are fully determined.

If this situation occurs at the edge of the minefield, you can use partial determinism to figure it out. But if it occurs in the middle of the board, you have to reason that if there are two mines in the three squares next to the "2", the only way they can be arranged to satisfy the "1"s is by placing the two mines away from each other.

I find it easier to just memorize this combination and attack it as soon as I see it.

The One-Two-Two-One
When two "2"s occur on a wall with "1"s on either side, forming a "1 2 2 1" combination, the mines are always adjacent to the "2"s. Figure 16 outlines the situation.

Figure 16
(a) A "1 2 2 1" situation. (b) The cells next to the "2"s can be flagged, and the cells next to the "1"s can be cleared.

The Prison Break
If you encounter a line of three "1"s which have a cleared "1" next to the center, you can make what I call the "prison break". Figure 17 outlines this situation. You can safely clear the three cells adjacent to the off-line "1", as shown below.

Figure 17
(a) The prison break situation. A line of three "1"s with a "1" adjacent to the center. (b) The cells adjacent to the off-line "1" can be cleared.

The Prison Break, Continued
If the next number just outside your prison break is also a "1", then you can clear an additional set of three cells. Figure 18 displays the outside "1", and the additional cells that may be cleared.

Figure 18
(a) The prison break with a "1" (marked in red) on the other side of the break. The additional set of cells that can be cleared is highlighted in pink. (b) The additional cells are cleared.

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