TECHNIQUE 1 OF 4
All remaining neighbours must be mines
A revealed clue becomes decisive when the number of mines still needed equals the number of its unresolved neighbours. Every one of those spaces must then contain a mine.
The rule
Count a clue's eight possible neighbours, including diagonals, and subtract established adjacent mines from its number. If the remaining count equals the number of unresolved neighbouring squares, mark all those squares as mines. Edge and corner clues simply have fewer neighbours; they do not use a different counting rule.
A common mistake
Subtracting an unproved flag can manufacture a false deduction. Also, hidden neighbours belonging to a different clue are irrelevant unless they actually touch the clue being analysed.
TRY IT 1 · mines-all-mines-1
| C1 | C2 | C3 | C4 | C5 | C6 | |
|---|---|---|---|---|---|---|
| R1 | ||||||
| R2 | ||||||
| R3 | ||||||
| R4 | ||||||
| R5 | ||||||
| R6 |
What can you justify?
Use the all remaining neighbours must be mines technique. What does it prove about R1C1? Treat the displayed starting marks as established facts, except flags, which the explanation must justify from revealed clues.
Written explanation
clue 1 at R1C2 still requires 1 mine among R1C1 after the established safe cells and proved mines are accounted for. Player flags are not used as evidence. Therefore R1C1 is a mine.
TRY IT 2 · mines-all-mines-2
| C1 | C2 | C3 | C4 | C5 | C6 | |
|---|---|---|---|---|---|---|
| R1 | ||||||
| R2 | ||||||
| R3 | ||||||
| R4 | ||||||
| R5 | ||||||
| R6 |
What can you justify?
Use the all remaining neighbours must be mines technique. What does it prove about R1C2? Treat the displayed starting marks as established facts, except flags, which the explanation must justify from revealed clues.
Written explanation
clue 2 at R2C3 still requires 2 mines among R1C3, R1C2 after the established safe cells and proved mines are accounted for. Player flags are not used as evidence. Therefore R1C2 is a mine.
One mine among two squares does not identify either
A revealed 2 has one proved adjacent mine and exactly two unresolved neighbouring squares A and B. Every other neighbour is known safe.
The tempting move
Mark both A and B as mines because the displayed clue is 2.
Why it fails
The proved mine already supplies one of the two. The unresolved pair contains exactly one additional mine, not two. Either local arrangement—mine at A or mine at B—meets the clue.
What is actually justified
Keep A and B unresolved unless other information distinguishes them. The all-mines rule does not apply because one mine remains but there are two candidate squares.
Transfer the idea
A revealed 3 touches one proved mine. All but two of its other neighbours are known safe. What must be true of those two unresolved squares?
Check your reasoning
Both are mines. The clue still requires two mines, and those are its only two possible locations. Merely flagging the first mine without proof would make the conclusion conditional on that flag being correct.