All Mines Accounted For
If a numbered clue already touches exactly that many correctly marked mines, every other adjacent covered cell is safe to reveal.
Why the highlighted cell is safe
- The corner clue is 1.
Exactly one of its adjacent cells contains a mine.
- One adjacent cell is already flagged.
The clue’s complete mine requirement is accounted for: 1 − 1 = 0.
- No other adjacent covered cell can be a mine.
Row 2, column 1—and the other covered neighbor beside that clue—can be revealed safely.
Calculate the remaining mines around any clue
For one revealed clue, collect every adjacent covered cell and count only the adjacent flags. Subtract those flags from the clue number. If the result is zero, every still-covered neighbor in that clue’s group is safe.
2 clue with 2 flags
2 − 2 = 0. Whether one or five other adjacent cells remain covered, none of them can contain another mine without violating the clue.
3 clue with 2 flags
3 − 2 = 1. One mine is still unaccounted for, so this direct rule proves no covered neighbor safe yet. Another clue or a subset comparison may resolve the group.
What Minesweeper Coach verifies
- Build the clue constraint.
The Solver records the clue’s currently covered neighbors and reduces its required mine count by the adjacent flags you entered.
- Reject impossible arithmetic.
A negative remaining count, or a count larger than the number of covered neighbors, is a contradiction rather than a move.
- Return a guaranteed reveal.
Only a constraint with zero remaining mines produces this rule’s safe-cell proof. If the visible clues do not force a move, the Solver says so instead of guessing.