Step 3 of 5

1-2 Pattern

When the shared cells can’t hold enough mines, the rest go outside them.

The rule of thumb: When the cells two numbers share can’t hold all the bigger number needs, the rest are mines in its other cells.

Take two neighboring numbers that share some hidden cells. The shared cells can hold at most as many mines as the smaller number still needs.

If the bigger number needs more than that, the extra mines must be in its own cells, the ones the smaller number doesn’t touch. When there are exactly that many, flag them all. Along a wall, a 1 next to a 2 means the cell past the 2 is a mine.

These boards can’t be finished without it.

Where to look: A 2 beside a 1 (or a 3 beside a 2) along an edge of hidden cells. Check the cell at the bigger number’s far end.

Worked example

A real position from a 8×8 board with 11 mines. Purple: the numbers the reasoning rests on. Dashed: the cells in question. Green: what it proves. Amber: the hidden cells the two numbers share.

The 3 at row 4, column 3 (purple) needs 2 more mines. The amber cells it shares with the 1 at row 5, column 3 can hold at most 1. The dashed cell is its only other hidden neighbor.

The 3 at row 4, column 3 needs 2 more mines, but the cells it shares with the 1 at row 5, column 3 can hold at most 1 (the 1 at row 5, column 3 needs only 1 more mine). So its other hidden neighbor is a mine.

Practice it ↓