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Minesweeper strategy

Advanced Minesweeper Patterns

Advanced positions rarely require a completely new rule. They combine subset comparisons, known flags, board geometry, and the remaining mine total. Reduce each clue to the mines it still needs, then compare the remaining candidate groups.

Diagram key Safe to reveal Mine to flagCovered and not yet resolved

Pattern reduction

A larger clue becomes a smaller effective clue after known adjacent mines are removed from its count. This reveals familiar patterns inside apparently complicated positions.

2-2 with one shared flag reduces to 1-1, making the extra cell safe.

Advanced

Reduced 1-1

These visible 2s each touch the same confirmed mine. Subtracting that flag turns the frontier into an effective 1-1.

  1. Subtract the shared flag from both 2s.
  2. Solve the remaining covered cells as a 1-1 safe extension.
The displayed 2-3 frontier reduces to 1-2 after accounting for the flag.

Advanced

Reduced 1-2

A neighbouring 2 and 3 that share one confirmed mine behave like 1 and 2 across their remaining covered cells.

  1. Remove the known mine from each clue mentally: 2 becomes 1 and 3 becomes 2.
  2. Apply the 1-2 extension to flag the unshared covered cell.
The flag reduces 2-3-2 to 1-2-1.

Advanced

Reduced 1-2-1

A row of 2-3-2 sharing one known mine becomes 1-2-1, producing the standard outside-mine, centre-safe result.

  1. Subtract the shared flag from all three clues.
  2. Solve the effective 1-2-1 before returning to the original values.

Corners and opposing subsets

At corners, independent arms can set minimum or maximum mine counts. Compare those arm totals with the corner clue to resolve the cell where the groups meet.

The marked corner cell supplies the third mine required by the 3.

Expert

1-3-1 corner

Each outer 1 allows at most one mine in its arm. The corner 3 therefore needs one mine from each arm and a third mine in the corner cell itself.

  1. Treat the horizontal and vertical arms as separate one-mine groups.
  2. Those groups supply only two of the central 3, forcing the diagonal corner candidate.
The two arm groups satisfy the central 2, leaving the marked corner safe.

Expert

2-2-2 corner saturation

After the outside 2s account for one mine in each arm, those two arm mines completely satisfy the middle 2. The corner candidate is safe.

  1. Use the outside clues and known flags to place one remaining mine in each arm.
  2. The central 2 is then full, so its additional corner neighbour cannot be a mine.
The middle covered cell is not needed by the 2 and can be revealed.

Expert

Opposing 1-2-1

Two outer 1s guarantee one mine on each side of a central 2. Those side groups use the entire mine count of the 2, making its remaining middle neighbour safe.

  1. Read each outer 1 as a separate one-mine group.
  2. Add the groups together: one plus one satisfies the central 2.

T-junctions and dependency chains

Longer positions connect several subset deductions. Work from constrained ends or branches, carry each result forward, and rescan the chain after every forced cell.

The 1-2-1-2-1 frontier resolves as alternating mines and safe cells.

Expert

Alternating dependency chain

A forced result at one end can alternate between mine and safe cells across the frontier until the whole chain is resolved.

  1. Start at an end where a 1 has only two covered neighbours.
  2. Feed each new mine or safe cell into the next clue instead of solving every clue independently.
The side branches each contribute one mine, so both unshared cells at the central junction are safe.

Expert

T-junction method

Where two chains meet, solve each branch as a mine group before returning to the junction clue. The junction then reveals whether its unshared cells are full, empty, or still unresolved.

  1. Record the mine total supplied by each branch, even when the exact mine positions are unknown.
  2. Subtract the branch totals from the junction clue and solve the remaining neighbours.

Endgame logic

Near the end of a board, the global mine counter becomes another constraint. It can settle isolated cells or disprove an otherwise plausible local arrangement.

Mines left2
The frontier accounts for both remaining mines, so the isolated marked cells are safe.

Endgame

Remaining-mine count

If every remaining mine is already accounted for inside known frontier groups, all other covered cells on the board are safe.

  1. Add the minimum mine totals of the unresolved groups without double-counting overlaps.
  2. When that sum equals the global mines remaining, reveal every covered cell outside those groups.
Mines left1
With one mine left, treating the marked cell as a mine forces an impossible second mine at the edge.

Endgame

Contradiction and combinations

When direct deductions stop, test a small number of candidate arrangements. Reject any assumption that breaks a clue or requires more mines than remain.

  1. Assume one candidate is a mine and propagate the consequences through nearby clues.
  2. If every continuation contradicts a clue or the mine total, the assumed cell is safe.
Core patterns Play Minesweeper