Minesweeper patterns

Every move on these boards follows from one of these. Each example is from a real board, with the owl's note.

Contents

  1. The count: as many squares as mines1
  2. The count: all its mines found2
  3. 1-13
  4. 1-24
  5. 2-25
  6. 1-36
  7. Shared squares7
  8. The total8

The rules

Each number counts the mines in the 8 squares around it. Open every square without a mine. Flag a square you know holds one. The rules, controls and boards

A pattern is named by what each number still needs once its flagged mines are counted: a 3 with two flags beside it counts as a 1.

The count: as many squares as mines

A number with as many unopened squares as mines it still needs: every one is a mine.

The 2 at E4 needs two mines, and D3 and D4 are its only unopened squares, so both are mines.

The count: all its mines found

A number whose mines are all flagged: every other square round it is safe.

The 2 at G5 already has both its mines flagged, so the other squares around it are safe: H4.

1-1

Two numbers that each need one mine, where the squares of one all lie inside the other's: the other's remaining squares are safe.

The 3 at E3 has its mine in D2 or F2. The 2 at E2 touches both of those too, and needs no more mines than that. So its other unopened squares, D1, E1 and F1, are safe.

1-2

The 2 needs one mine more than the 1 beside it. When it has exactly one square the 1 does not touch, that square is a mine.

The 2 at A4 has its mine in A3 or B3. The 3 at B4 touches both of those too, and needs one more mine besides, so C3 is a mine.

2-2

The 1-1 with two mines each: the bigger number's other squares are safe.

The 4 at F11 has its two mines in E10, E11 and E12. The 2 at D11 touches all of those too, and needs no more mines than that. So its other unopened squares, D10, C12 and D12, are safe.

1-3

The 1-2 with two mines more: as many squares of its own as extra mines, so all are mines.

The 3 at D4 has its mine in C3 or C4. The 4 at D3 touches both of those too, and needs two more mines besides, so C2 and D2 are mines.

Shared squares

Two numbers overlap without one containing the other: the overlap can hold only so many mines.

The 3 at G3 needs two more mines among F2, G2 and H2. H2 can hold only one, so there is a mine in F2 or G2. That is the only mine the 1 at F3 needs, so E2 is safe.

The total

Near the end, the mines left over the whole board.

The one mine left must be in the last square.

When to guess

Every board here can be cleared without a guess: a board is kept only if these patterns clear it from the first square.

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