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Minesweeper Subsets: The 1-1 Pattern

The subset technique says: when every hidden square around one number also touches a second number, compare them. The first number’s mines are all in the shared squares, so the second number’s own squares hold whatever it still needs beyond that. If that’s nothing, they’re safe; if it’s all of them, they’re mines. Its best-known form is the 1-1 pattern.

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This is the third of the Minesweeper techniques.

The rule

  1. Find two numbers next to each other, and take the flags off both: work with what each still needs.
  2. Check that all of the first number’s hidden squares also touch the second.
  3. The second number’s other squares hold its need minus the first number’s need. If that’s 0, open them. If it equals how many there are, flag them.
Subset: the 1-1 pattern at the edge A row of hidden squares over a row of numbers. The first 1 touches only the first two hidden squares, and the second 1 touches those two and a third. The mine is in the first two, so the third square is safe. 1 1 1 1 2 2 1
The first ringed 1 touches two hidden squares, both shared with the second 1. Its mine is one of them, so the second 1’s third square (dotted) is safe.

In a real game

On the Expert board every technique page follows, the simple checks run dry for the first time at step 27. A 3 with two flags needs one more mine, from two hidden squares. The 1 beside it touches those two and a third, and its mine is the same one. So the third square is safe: a 1-1, once the 3’s flags are taken off.

Step 27: a subset Part of the Expert board at step 27. A 3 with two flags needs one more mine, from two hidden squares that the 1 beside it also touches. The 1's mine is the same one, so its third square is safe. 2 1 3 1 1 2 2
Step 27: the ringed 3 works like a 1, and with the ringed 1 it makes the dotted square safe.

How often you’ll need it

On 51 of 200 Beginner boards, 125 Intermediate and 172 Expert, which makes it the most important technique after the two simple checks. On the Expert board here it’s needed 15 times.

Next steps

Questions

What's the 1-1 pattern?

Two 1s side by side, where one of them touches only squares the other touches too. The first 1’s mine is one of those shared squares, so it’s the second 1’s mine as well, and the second 1’s other squares are safe.

Can a subset find mines as well as safe squares?

Yes. If the bigger number needs more mines than the shared squares can hold, its extra squares are mines. A 1 and a 2 at the edge of a wall is the usual case.