Every Minesweeper number pattern, with the proof behind each one

How we got these numbers

Every result below is derived from first principles for the standard wall configuration and checked for uniqueness by exhausting the possible mine placements, not taken from other guides. Board dimensions, mine counts and the number colours are read from the shipped source, src/lib/minesweeperBoard.ts and src/pages/Minesweeper.tsx, as of 12 August 2026.

The setup every pattern assumes

Almost every named Minesweeper pattern describes the same situation: a row of revealed numbers with a solid run of unopened cells directly in front of them, and nothing unopened anywhere else that those numbers touch. Players call it a wall. If you do not fix that setup, the patterns are not true, which is why so many guides quietly disagree with each other.

Number the unopened wall cells W1, W2, W3 and so on, left to right. The first number of the pattern sits above W2, the second above W3, the third above W4. Each number therefore touches exactly three wall cells: the one directly in front of it and the two diagonally either side. A pattern of k numbers faces k plus 2 wall cells.

One more condition, and it is the one people forget. Each number's count must be fully explained by the wall. If a number also touches an unopened cell behind it or above it, none of what follows applies to that number. Check the whole ring of eight before you trust a pattern.

Wall notation used throughout: k numbers in a row face wall cells W1 to W(k+2). Number i sits above W(i+1) and touches W(i), W(i+1) and W(i+2).

The one rule that generates all of them

Take two numbers that sit next to each other on the wall. Call the left one N and the right one M. N touches W(i), W(i+1) and W(i+2). M touches W(i+1), W(i+2) and W(i+3). They share two cells, W(i+1) and W(i+2).

Write each cell as 1 if it hides a mine and 0 if it does not. Then N is the sum of its three cells and M is the sum of its three. Subtract, and the two shared cells cancel exactly:

M minus N equals W(i+3) minus W(i).

That is the whole thing. The left side is a number you can read off the board. The right side is a difference of two values that are each either 0 or 1, so it can only ever be minus 1, 0 or plus 1. Three cases, and each one is decisive.

Applies to any two horizontally adjacent numbers facing the same clean wall. The named patterns below are this rule applied once, twice or three times.

Two numbers next to each other on the same wall can never differ by more than 1. If you think you are looking at a 1-3-1, one of those numbers is seeing something you have not accounted for.

The fully forced patterns

These have exactly one solution. Every wall cell in front of them is determined, and no guessing is involved. Work them until they are automatic, because they are the ones that pay.

Take 1-2-1 as the worked example. The differences are plus 1 then minus 1. The plus 1 forces W4 to be a mine and W1 to be clear. The minus 1 forces W5 to be clear and W2 to be a mine. The middle 2 now has mines at W2 and W4 already, which uses up its whole count, so W3 is clear. Five cells resolved from two subtractions.

3-2-1 is even quicker. A 3 facing three wall cells means all three are mines with no arithmetic at all, and the two minus 1 differences then clear W4 and W5.

Each row was checked by enumerating all placements consistent with the counts. In every case exactly one survives.

• 1-2-1 puts the mines under the 1s. 1-2-2-1 puts them under the 2s. Learning one and assuming the other is the most common misplay in the whole game.
• 2-1-2 is the mirror of 1-2-1 in a way that surprises people: the mines land on the outer wall cells and under the middle number, not under the 2s.
• 2-1-1-2 is 2-1-2 stretched by one. The two middle cells are clear and both ends are fully mined.
• In every fully forced pattern the outermost wall cells are resolved too. Players routinely take the middle result and walk away from two free cells at the ends.

The partly forced patterns

These are the ones that generic guides get wrong, because they either claim a full solution that does not exist or say the pattern is useless. Both are false. Each of these resolves some cells for certain and leaves the rest as a genuine coin flip.

1-2-2-2-1 is the clearest case. The outer differences are plus 1 and minus 1, which force W4 to be a mine and both W1 and W7 to be clear. The two inner differences are zero, which links W2 to W5 and W3 to W6 without resolving either. Two arrangements satisfy everything: mines at W3, W4 and W6, or mines at W2, W4 and W5. Nothing on the wall alone can separate them.

That is worth knowing precisely, because the wrong response to a 50/50 is to stare at it. The right response is to flag W4, open W1 and W7, and go and find information somewhere else on the board. Often a number one row further out settles it for free.

Counts obtained by enumerating every assignment of mines to the wall cells that satisfies all the numbers simultaneously.

A pattern that only half resolves is still worth playing. Take the certain cells, then leave. The mistake is spending a minute trying to force a position that is provably undecidable.

Runs of 1s, and why they need an anchor

1-1, 1-1-1 and 1-1-1-1-1 are among the most searched shapes and the most misunderstood, because on their own they force nothing at all. Every difference in a run of 1s is zero, so the rule above only ever links cells together. It never resolves one.

What makes a run of 1s useful is an anchor: one end of the wall already known. The board edge is an anchor. So is a cell you have already opened, or one you have already flagged and accounted for. With the left end anchored clear, the arithmetic starts to bite.

Anchor W1 as clear. The first 1 then needs its single mine among W2 and W3. The second 1 sees W2, W3 and W4, and its single mine is already sitting in W2 or W3, so W4 must be clear. Two 1s is all that takes.

Now W4 is a known clear cell, which is a fresh anchor, and the argument restarts from there. Extend the run to five 1s and the same reasoning three cells further along clears W7. Every third cell, as far as the run reaches.

• In a run of 1s anchored at one end, every third wall cell from the anchor is clear: W4, then W7, then W10, as far as the run of 1s extends.
• The run does not need to be long. Two 1s against a board edge already give you a free open. Reaching W7 needs five.
• The anchor can be a flag rather than a clear cell. Anchoring on a flag flips the arithmetic, so redo the subtraction rather than reusing the result.
• Without an anchor at either end, a run of 1s is genuinely undecidable no matter how long it is. Length does not help. Go and find an edge.

1-1-1 is not a pattern about the number 1. It is a pattern about the wall having an end. Find the end first.

Patterns that cannot exist

Some of the shapes people search for cannot occur in the wall configuration at all, and knowing that is faster than trying to solve them.

1-3-1 is the main one. Adjacent numbers on a clean wall differ by at most 1, and 3 minus 1 is 2. Read it directly: the 3 needs mines in all three of W2, W3 and W4, but the left 1 touches W1, W2 and W3 and would then be seeing two mines. It is a contradiction, not a hard puzzle.

If a 1-3-1 appears to be on your screen, one of three things is true. The 3 is also touching an unopened cell behind or above it, so the wall does not explain its count. Or one of the 1s is, for the same reason. Or the wall is broken by an already-opened cell between them, in which case they are not adjacent in the sense the rule requires and the difference restriction does not apply.

The same test rules out 1-3, 2-4, 0-2 and any other adjacent pair separated by two or more. Use it as a proofreading tool: if the wall shows an impossible jump, stop solving and re-examine what those numbers actually touch.

What the numbers and their colours mean here

A number is the count of mines in the eight cells surrounding it, nothing else. A cell showing nothing at all is a zero, and because it has no mines around it the game opens its neighbours for you, which is where cascades come from.

Daily Minesweeper colours the counts so you can read density at a glance rather than reading digits. The palette is fixed and worth learning, because at speed you are pattern matching on colour, not on shape.

Read from the colour map in src/pages/Minesweeper.tsx as shipped on 12 August 2026.

The board you are actually playing

Pattern frequency depends on mine density, so it is worth knowing which board you are on. The daily rotates between Medium and Easy on alternating days, and all three sizes are available in practice.

Densities computed from the difficulty table in src/lib/minesweeperBoard.ts.

• Mines are placed after your first click, avoiding that cell and, where there is room, all eight of its neighbours. Your opening move cannot lose and usually opens a region.
• Open near the centre. A central first click excludes nine cells from the mine pool instead of four, and gives you a wider frontier to run patterns against.
• Higher density means more 2s and 3s, which means more fully forced patterns, not fewer. Hard boards are more solvable per square than they look.
• Mine placement is uniformly random over the eligible cells. There is no bias toward corners or edges to exploit, and no reason to believe one region is safer than another before you have numbers.

How to use this at speed

• Open in the centre, then flag and open everything that is immediately satisfied before looking for any pattern at all.
• Walk the frontier left to right and subtract each adjacent pair of numbers. Every plus 1 or minus 1 resolves two cells instantly.
• Only reach for a named pattern when the subtraction leaves you flat. The names are a shortcut for shapes you meet often, not a separate skill.
• When a shape resolves only partly, take the certain cells and move on immediately. Do not try to break a 50/50 by looking harder at it.
• If a difference of 2 or more appears, treat it as a reading error and re-check what those numbers touch before doing anything else.
• Track the remaining mine counter. Late in a Hard board it is frequently stronger evidence than anything on the frontier.

The whole method in one line: subtract adjacent numbers, act on every plus or minus 1, and only name a pattern when subtraction runs out.

Frequently asked questions

What does the 1-2-1 pattern mean in Minesweeper?

Against a clean wall of unopened cells, a 1-2-1 forces mines directly under the two 1s and leaves the cell under the 2 clear. The two outer wall cells, the ones diagonally outside each 1, are also clear. It is the single most useful forced shape on our board sizes.

What is the 2-1-2 pattern?

The opposite arrangement to 1-2-1. Mines land on the two outer wall cells and on the cell directly under the middle 1, while the cells under both 2s are clear. It is fully forced with exactly one solution.

Is there a 1-3-1 pattern in Minesweeper?

No. Two numbers next to each other on the same wall can never differ by more than 1, so 1-3-1 cannot occur. If you appear to be looking at one, at least one of those numbers is also touching an unopened cell that is not part of the wall, or the wall is broken between them.

What does 1-1-1 tell you?

On its own, nothing. A run of 1s only becomes solvable when one end is anchored by a board edge or an already-resolved cell. With the left end anchored clear, every third wall cell from the anchor is clear, as far as the run of 1s reaches: two 1s clear the fourth cell, five 1s also clear the seventh.

Does the 1-2-2-2-1 pattern have a unique solution?

No. It forces a mine under the middle 2 and clears both outer wall cells, then leaves a genuine 50/50 between two arrangements. Take the three certain cells and look elsewhere on the board rather than trying to break the tie.

Why does 2-2-2 give me nothing?

Because all the adjacent differences are zero, which links cells rather than resolving them, and three separate mine arrangements satisfy the counts. It is the clearest example of a shape that looks informative and is not.

Do I need to memorise all of these?

No, and it is faster not to. Every pattern here follows from subtracting adjacent numbers on the same wall. Learn the subtraction and you can solve shapes that have no name, including ones with 4s and 5s that no guide lists.