All Covered Cells Are Mines
If a clue still requires exactly as many mines as it has adjacent covered cells, every one of those covered cells must be a mine.
Why the highlighted cell is a mine
- The corner clue is 3.
Its adjacent cells must contain three mines in total.
- Two adjacent mines are already marked.
The clue still requires one mine: 3 − 2 = 1.
- Only one adjacent covered cell remains.
One required mine in one unknown cell forces that cell to be a mine.
Match remaining mines to remaining cells
For one revealed clue, subtract its adjacent flags from the clue number, then count its adjacent covered cells. When those two values are equal, every cell in that covered group must be a mine.
2 mines in 2 cells
A clue still needs two mines and has exactly two covered neighbors. Both cells are forced mines; no alternative placement can satisfy the clue.
2 mines in 3 cells
Two of the three cells are mines, but the direct rule cannot identify which two. Keep all three covered until another clue or a subset comparison adds information.
Why the conclusion is deterministic
- Reduce the clue by known flags.
The Solver turns each visible clue into a remaining-mine requirement over only its adjacent covered cells.
- Compare requirement and group size.
If a group of n cells still requires n mines, the only satisfying assignment places a mine in every cell.
- Return flags, not reveals.
The result names each forced mine as a flag move. Those new facts can then reduce neighboring constraints and expose guaranteed safe cells.