Minesweeper

Board, numbers, and flags

This Minesweeper board is a 9-by-9 grid containing 10 hidden mines. Open a safe cell to reveal either a number or an empty area. Opening a mine ends the game. You win when every non-mine cell is open; mines do not all need to be flagged.

Each number counts mines in the surrounding eight cells, including diagonals. A 1 touches exactly one mine, a 2 touches exactly two, and so on. A blank or zero has no adjacent mines, so the game automatically opens the connected blank region and its numbered boundary.

| Visible situation | Certain conclusion | |---|---| | A number has that many flagged neighbours | All its other covered neighbours are safe | | A number has exactly that many covered neighbours left | Every one of those covered cells is a mine | | A zero touches covered cells | Those cells are safe and open automatically | | All non-mine cells are open | The board is won, regardless of flags |

Flag mode marks or unmarks a covered cell. A flag is only your assertion: the game does not validate it until the board is resolved. You cannot open a flagged cell, so remove a flag if later logic disproves it.

The first open is protected. If that cell was mined, the mine moves elsewhere and all numbers are recalculated. Unlike versions that guarantee a large blank opening, only the selected cell is guaranteed safe here.

Frontier logic and pattern deductions

Expand the information frontier

The best opening result is a blank region because it reveals many numbers at once. Corners and edges have fewer neighbours and can be easier to analyse, while central cells have a better chance to connect with more space; no location guarantees a zero. After the first click, work along the boundary where open numbers touch covered cells. Clicking far into an unknown area adds risk without using the information already earned.

For every boundary number, perform two counts:

1. How many adjacent mines are already flagged?
2. How many adjacent cells remain covered and unflagged?

Subtract flagged mines from the displayed number. The result is the number of mines still hidden among the unflagged neighbours. If the result is zero, open all of them. If it equals the number of covered neighbours, flag all of them.

For example, if a 3 touches two flags and three other covered cells, exactly one of those three remains mined; that is useful but not yet enough to select a specific cell. If it touches two flags and only one other covered cell, that last cell must be the third mine.

Compare overlapping number sets

Many boards stall because no single number is complete. The next step is subset reasoning. Treat each number’s unknown neighbours as a set.

Suppose one 1 touches covered cells {A, B}, while a nearby 2 touches {A, B, C}. Because exactly one mine lies among A and B, and exactly two lie among A, B, and C, C must be a mine. The reverse works too: if both sets require one mine, the extra cell C must be safe.

The familiar edge pattern 1-1 often produces this relationship, but do not memorise a visual slogan without checking neighbours. Flags elsewhere may change the remaining counts. Always compare the actual covered-cell sets after subtracting known mines.

Use flags to simplify, not to speculate

Flag a cell only when logic proves it is mined. Correct flags reduce the remaining count around several numbers and frequently trigger safe openings. Speculative flags are dangerous because later reasoning treats them as facts.

After placing any flag, revisit every adjacent number. One new mine can complete a 1, 2, or 3 and make all its other neighbours safe. Likewise, after opening a safe cell, inspect its number before moving elsewhere. Minesweeper rewards local chains of deductions.

Some players prefer minimal flagging and mentally track mines. That can be fast, but on a larger frontier flags reduce working-memory errors. The important distinction is confidence: use flags as confirmed constraints, not guesses.

Analyse edges and corners carefully

Numbers on the boundary have only three or five possible neighbours rather than eight. This often makes their constraints tighter. A corner 1 with one flagged neighbour immediately clears its other adjacent cells.

However, avoid assuming that the outermost covered cell is safe merely because few cells touch it. The number describes mines around the open numbered cell, not around the covered candidate. Draw the exact eight-cell neighbourhood mentally, especially for diagonal contact.

Recognise when logic is exhausted

A position can be ambiguous. Two covered cells may each be equally capable of holding the final mine, with no other number distinguishing them. Before guessing, scan the entire frontier for a separate deduction that could reveal new information. A safe opening elsewhere may resolve the apparent 50–50.

If a guess is truly necessary, estimate risk. A cell constrained to one mine among three possibilities has roughly lower risk than one in a forced one-of-two pair, assuming no additional constraints. Prefer guesses that are likely to reveal a useful region if safe. Do not place a flag simply to disguise uncertainty; open the best candidate with a clear understanding that it is probabilistic.

Mistakes that turn logic into guesses

Reading a number as a distance. A 2 does not mean a mine is two spaces away. It means exactly two of the immediately touching eight cells are mines.

Forgetting diagonal neighbours. Most false deductions come from counting only horizontal and vertical cells. Trace the full ring around each number.

Treating flags as game-confirmed. Flags are player notes. One wrong flag corrupts every nearby calculation, so recheck them when a contradiction appears.

Opening random covered cells too early. Exhaust the visible frontier first. Basic completion and subset comparisons often reveal a safe move that is not visually obvious.

Looking at one number in isolation. An unresolved 1 may become decisive when compared with a neighbouring 1 or 2. Overlapping constraints are the core of intermediate play.

Failing to update after a flag. Every confirmed mine changes all adjacent equations. Rescan those numbers immediately rather than moving to a distant part of the board.

Assuming every position has a deduction. When multiple layouts fit all evidence, logic cannot select between them. Verify globally, then make the lowest-risk guess instead of inventing certainty.

Frequently asked questions

What do the numbers in Minesweeper mean?

A number tells you exactly how many mines occupy the eight cells touching it horizontally, vertically, or diagonally. It does not describe an entire row or the nearest mine.

Do I have to flag every mine to win?

No. You win by opening every non-mine cell. Flags are notes that help prevent mistakes; a wrongly placed flag can block progress but does not turn that cell into a mine.

Is the first click safe?

Yes. If the first selected cell contains a mine, this version relocates that mine. The first cell is safe, although it is not guaranteed to be a zero or open a large area.

Are all Minesweeper boards solvable without guessing?

Not necessarily. Some positions leave two or more mine arrangements equally consistent with every visible number. Use all available deductions first, then choose the lowest-risk cell when a guess is unavoidable.