Minesweeper strategy: the patterns that solve most of the board

Minesweeper strategy comes down to one habit: never click a cell until the numbers prove it is safe. Every number tells you how many mines touch it, and when you compare two neighbouring numbers, the difference between them usually settles a cell or two. A handful of recurring shapes — the 1-1, the 1-2, the 1-2-1 and the 1-2-2-1 — solve most of a board on sight. Here is how to play minesweeper by reading them.

What the numbers mean

Every opened cell shows how many of the eight cells around it — up, down, left, right and the four diagonals — contain a mine. A cell on an edge has only five neighbours, and a corner cell only three. Open a cell with no mines around it and the game opens its neighbours for you, which is why a good first click spills open a whole clear patch.

The thing that turns a number into a tool is this: once you know where some of its mines are, the number shrinks. A 3 with two flagged neighbours is really a 1 among its remaining hidden cells. Almost every deduction in the game is that subtraction, done quickly.

The first click

On BrainBreak the first cell you open is always safe, and the mines are laid only after you choose it, keeping its whole neighbourhood clear. So your first click always opens a patch rather than a single number. Where you click does not matter much; the middle of the board tends to give the most room to work with.

Flagging, and why it matters

A flag is a note to yourself: “I have proved there is a mine here.” The game never checks flags and they never open anything, but they make the subtraction above visible. With a flag in place, you can read each neighbouring number as “how many mines are still unaccounted for”.

Only flag what you have proved. A flag you merely suspect is worse than no flag, because every later deduction built on it inherits the doubt. On a phone, hold a cell to flag it, or switch the Dig / Flag control and tap; with a mouse, right-click.

Chording: the move that makes you fast

Once a number has as many flags around it as its value, every other hidden neighbour must be safe. Instead of opening them one at a time, you can chord: press the number itself and all its unflagged neighbours open at once. Tap an opened number on a phone, middle-click or press both buttons with a mouse, or press C on a keyboard.

Chording trusts your flags completely. If one of them is wrong, the chord opens a mine. That is the best argument there is for flagging only what you have proved.

How to read the diagrams

In the patterns below, # is a hidden cell, · is an opened cell whose number does not matter here, * is a cell the pattern proves is a mine and S is a cell it proves is safe. A | is the edge of the board. In each case, assume the row of numbers sits on the boundary of what you have opened: the only hidden cells they touch are the ones drawn in the row above.

The 1-1 pattern at a wall

| #  #  S
| 1  1  ·

The first 1 is against the wall, so it touches only the first two hidden cells, and exactly one of them is a mine. The second 1 touches those same two cells plus the third. It also sees exactly one mine — and that mine is already accounted for by the first two cells. So the third cell is safe. Open it.

The general lesson: when one number’s hidden cells are a subset of another’s, and the two numbers are equal, everything in the bigger set that is not in the smaller one is safe.

The 1-2 pattern

At a wall first:

| #  #  *
| 1  2  ·

The 1 sees two cells with one mine between them. The 2 sees those two cells and one more. Only one of its mines can be in the shared pair, so its second mine must be the third cell. Flag it.

The 1-2 works away from a wall too, and there it proves two things at once:

  S  #  #  *
  ·  1  2  ·

The 1 sees the first three hidden cells; the 2 sees the middle two and the fourth. At most one mine can sit in the middle two (the 1 allows no more), so the 2 needs the fourth cell to be a mine. And because the middle two then hold exactly one mine, that uses up the 1 — so the first cell is safe. Whenever you see a 1 next to a 2 along a straight edge, look at both ends.

The 1-2-1 pattern

  S  *  S  *  S
  ·  1  2  1  ·

This is the most famous shape in the game, and it resolves completely. Read it as two overlapping 1-2 patterns. The left 1 and the 2 form a 1-2 facing right, which proves the cell above the right-hand 1 is a mine and the cell at the far left is safe. The 2 and the right 1 form a 1-2 facing left, which proves the cell above the left-hand 1 is a mine and the cell at the far right is safe. The 2 now has both its mines, so the cell directly above it is safe too.

The short version is worth memorising: in a 1-2-1, the mines sit above the 1s, and the cell above the 2 is clear.

The 1-2-2-1 pattern

  S  S  *  *  S  S
  ·  1  2  2  1  ·

Same idea, stretched by one. The left 1 and the first 2 form a 1-2 facing right, which puts a mine above the second 2 and clears the far-left cell. The right 1 and the second 2 form a 1-2 facing left, which puts a mine above the first 2 and clears the far-right cell. Those two mines satisfy both 1s as well, so the cells above the 1s are safe. In a 1-2-2-1, the mines sit above the 2s.

Subtracting constraints: the pattern behind the patterns

Every shape above is one idea applied to a straight edge. Take two numbers that share some hidden cells. Subtract any flags already around them. Then compare:

• If one number’s hidden cells all belong to the other number as well, the difference in their values is the number of mines in the cells only the bigger one can see.
• If that difference is zero, those extra cells are all safe (the 1-1).
• If it equals the number of extra cells, they are all mines (the 1-2 at a wall).

Here it is around a corner rather than along a straight edge:

  S  S  S
  #  1  ·
  #  1  ·
  ·  ·  ·

The lower 1 touches only the two hidden cells on the left, so its one mine is in that pair. The upper 1 touches that same pair and the three cells above it. Its single mine is already spoken for by the pair, so the difference is zero and all three cells along the top are safe. Nothing about this is a named pattern — it is just the 1-1 idea turned through a right angle.

When you are stuck, do this by hand: pick two neighbouring numbers, list the hidden cells around each, subtract any flags, and compare what is left against the difference in their values. After a few boards the named patterns stop being things you memorise and start being things you simply see.

Every BrainBreak board can be solved without guessing

In many versions of minesweeper, a game can come down to two cells the numbers cannot tell apart, and you lose to a coin flip after playing perfectly. BrainBreak checks every board with a solver before you see it and deals another if the numbers alone cannot finish it. So if you are stuck, you have not run out of luck; there is a deduction waiting — usually one of the shapes above, or a subtraction between two numbers you have not compared yet.

Three boards are on offer: Small (9 by 9, 10 mines), Medium (12 by 12, 22 mines) and Large (16 by 16, 40 mines). Each keeps its own game and its own best time.

More deduction puzzles

If you enjoy the “what must be true?” feeling, you will probably like Nonogram and Sudoku, which reward exactly the same refusal to guess. Our round-up of logic games that make you think has more.