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Minesweeper Pairs: The 1-2 Pattern

The pair technique says: when two numbers share some hidden squares, but each also has squares of its own, work out how many mines the shared squares can hold. That’s limited by both numbers, and the limit often settles the squares only one of them touches. Its best-known form is the 1-2 pattern.

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This is the fourth of the Minesweeper techniques.

The rule

  1. Find two numbers whose hidden squares overlap, and take the flags off both.
  2. The shared squares can hold no more mines than the smaller need, and no more than there are shared squares.
  3. If the bigger number needs more than that, the rest are on its own squares: if that fills them, they’re mines. And if the smaller number’s mine has to be in the shared squares, its own squares are safe.
Pair: the 1-2 pattern Part of an Intermediate board. A 2 and a 3 side by side, with a flag below the 2. The 2 needs one more mine and the 3 needs two, from the hidden row above. The 2 can give the shared squares at most one, so the 3's own square is a mine and the 2's own square is safe. 3 2 3 1 3 2 1
Part of an Intermediate board. The ringed 2 needs one more mine and the ringed 3 needs two, from the hidden row above.

In a real game

On the Expert board every technique page follows, the first pair comes at step 30. A 3 with one flag needs two more mines, and the 1 beside it needs one. They share two hidden squares, which can hold at most one mine, because of the 1. So the 3’s own square is its other mine, and the 1’s own square is safe.

Step 30: a pair Part of the Expert board at step 30. A 3 with one flag needs two more mines, and a 1 beside it needs one. They share two hidden squares, which can hold only one mine because of the 1. So the 3's own square is a mine and the 1's own square is safe. 4 3 1 1 3 1 1 2
Step 30: the ringed 3 (needing two) and 1 (needing one) settle a mine on the left and a safe square on the right.

How often you’ll need it

On 4 of 200 Beginner boards, 18 Intermediate and 114 Expert. On Beginner it’s rare, but on Expert it comes up on more than half the boards. On the Expert board here it’s needed 3 times.

Next steps

Questions

What's the 1-2 pattern?

A 1 next to a 2 (after taking off flags), sharing some hidden squares. The shared squares can hold at most one mine, because of the 1, so the 2’s own square must be its second mine, and the 1’s own square, if it has one, is safe.

How is this different from a subset?

In a subset, all of one number’s hidden squares touch the other. In a pair, each number also has squares of its own. The idea is the same: work out what the shared squares can hold.