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You can find many hidden mines by treating every revealed number as a constraint: count its covered neighbours, subtract mines already identified, then mark the remaining cells that must be safe or mined. Comparing overlapping clues often reveals moves that a single number cannot. But classic Minesweeper does not guarantee a deduction for every position; when the clues cannot prove a safe move, you may have to weigh probabilities.
Start with what each number proves
A number counts the mines among the covered cells touching it, including diagonals. For each clue, count only its still-covered neighbours and subtract any mines you have already established. The remainder is the number of mines still required in those cells.
- If the remaining mine count is zero, every covered neighbour of that clue is safe.
- If the remaining mine count equals the number of covered neighbours, every one of those cells is a mine.
For example, if a 3 touches two marked mines and two covered cells, it still needs one mine among those two cells; that clue alone does not tell you which one. If it touches two marked mines and just one covered cell, that last cell must be a mine. After you establish a safe cell or mine, revisit nearby clues: the new information may force another move.
Compare clues that share covered cells
When individual clues do not settle a move, compare the sets of covered cells they touch. If one clue’s covered-neighbour set is contained within another’s, subtract the smaller set and its mine requirement from the larger one. The extra cells must contain the difference in mines.
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Suppose a clue constrains two covered cells to contain one mine, while a nearby clue constrains those same two cells plus a third covered cell to contain two mines. The shared pair account for one mine, so the third cell must contain the other. This is subset reduction: it is the logic behind several familiar patterns, and it still works when a board does not match a memorized shape exactly.
You can also simplify a clue before comparing it: subtract mines already identified from its number and remove those cells from its covered-neighbour set. The Minesweeper Online patterns guide illustrates how constraints that initially look like 2 and 4 can reduce to simpler 1-count relationships after known mines are accounted for. See the Minesweeper Online patterns guide.
Use edge patterns only when the cell layout matches
Pattern names are shorthand for particular arrangements of covered cells. The numbers alone do not establish the answer: first verify exactly which hidden cells each clue touches. The following outcomes apply to the standard straight-wall arrangements described in the cited guides.
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1-2 at a wall
In the common arrangement, the 1 and 2 share two covered neighbours, and the 2 touches a third cell beyond that pair. The 1 requires one mine in the shared pair. The 2 requires two mines across the pair and the extra cell, so that extra cell must be a mine. This is often called the 1-2-X rule.
1-2-1
In the standard wall arrangement, apply the 1-2 deduction from each end. The result across the three relevant covered cells is mine, safe, mine. Do not apply this sequence if the clues touch a different set of hidden cells.
1-2-2-1
In its standard wall arrangement, deductions from both ends establish the four relevant cells as safe, mine, mine, safe. As with 1-2-1, the covered-cell geometry is essential.
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1-1 along a boundary
In the standard 1-1-X arrangement, both 1s constrain the same two covered cells, while the second 1 also touches an extra covered cell. Since the shared pair already contain the one mine required by each clue, the extra cell is safe.
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When deduction runs out
Some classic Minesweeper positions have no move that the visible clues prove safe. The Minesweeper.org strategy guide notes that logic alone cannot solve every position, and an August 2008 Decision Analysis Newsletter article discusses choosing tiles under uncertainty using conditional probability.
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If no safe move is forced, compare the possible mine layouts consistent with all revealed clues. When survival is your only aim, choose a cell with the lowest mine probability. If different reveals would expose different amounts of useful information, that information may also matter. There is no universally best choice without the board state and your objective.
That distinction matters when choosing a game mode. A “no-guess” label describes a generator’s rules, not a property of Minesweeper as a whole. Minesweeper Co-op says its generator tests candidate boards with a solver that makes only provably safe moves, discards candidates that get stuck, and operates subject to an attempt limit and other stated caveats. Its page reports these solvable-candidate rates for its own 20×16 boards; the page does not state a publication year:
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|---|---|
| 18.8% | 17% |
| 20.6% | 7% |
| 22% | 3% |
| 24% | 0.3% |
These figures describe that service’s candidate generation and checks; they are not general rates for Minesweeper boards or a guarantee about other games. Minesweeper Co-op explains its rules and no-guess boards.
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Practise the deductions, not just the sequences
Minesweeper Co-op offers untimed drills with one deduction per board and feedback about the rule used. Listed exercises cover direct counting, 1-1, 1-2, 1-2-1, 1-2-2-1, subset reduction, and patterns in a more realistic-looking position. Use them to practise identifying which covered cells each clue constrains, then transfer that counting habit to unfamiliar boards; matching a number sequence from memory is not enough.
For a broader view of solver techniques, Yimin Tang, Tian Jiang, and Yanpeng Hu’s 2018 preprint describes logic inference, constraint satisfaction, and sampling as approaches to solving Minesweeper. Read the preprint on arXiv.
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