Minesweeper Patterns: 1-1, 1-2-1, 1-2-2-1 and Corners

How to read this guide

A pattern is a group of numbers along the border between open and closed cells. It is not a new rule: it is what careful reasoning gives every time the same numbers meet the same closed cells. Knowing the result saves the reasoning, but only when the picture matches exactly.

The explanations use the words of the techniques guide. For every open number, two things matter: how many mines it still needs, and which closed cells around it are still undecided. Rule 1 counts around one number. Rule 2 compares two numbers when all undecided cells of one of them belong to the other.

• Minesweeper techniques: the three rules

In the diagrams, closed cells are tinted; the ones the text talks about carry a letter. A flag marks a proven mine and a ring a proven safe cell. A thick line is the edge of the board, a dashed line means that the board goes on, and a dash marks an open cell whose number does not matter for the pattern.

Practice boards: press a closed cell once for a mine, twice for safe, a third time to clear it (keys: arrows, M, S, Backspace). Leave undecidable cells unmarked, then press Check.

1-1 and 1-2 at the edge of the board

Along the edge of the board a number touches fewer cells. In the diagram, the first 1 sits on the left edge, so its only undecided cells are A and B. The 1 beside it touches A, B and C.

Rule 2 applies: all undecided cells of the first 1 belong to the second. The first 1 needs one mine in A or B, and that is also the one mine of the second 1. The extra cell C gets 1 − 1 = 0 mines, so it is safe. Which of A and B holds the mine is still undecided.

Put a 2 in place of the second 1, and the extra cell gets 2 − 1 = 1 mine: C is a mine. These are the first two rows of the table under rule 2 in the techniques guide.

The board edge is not the only thing that cuts a number short. A flag is a mine already found, and an open neighbour is not undecided, so a 2 with one flag on its outer side, whose only undecided cells are the two it shares with its neighbour, plays the part of the edge 1.

On this practice board the numbers lie on the bottom edge, and the cell to the right of the second 1, D, is closed. D is safe for the same reason as C.

Around a corner: two 1s and the number between them

Where the open area turns a corner, the numbers along the two sides can account for the number in the corner between them. In the diagram, the open area is the top-left corner of the board. The 1 at the top has only P and Q undecided, the 1 on the left only R and S, and the 2 in the corner touches all four and K, the closed cell diagonally below and to the right of it.

The 1 at the top puts one mine in P or Q, and the 1 on the left one mine in R or S. All four cells touch the 2, so it already has its two mines, and K is safe; with a 3 in the corner, K is a mine. In the words of rule 2: comparing the top 1 with the 2 leaves one mine in R, S and K, and comparing the left 1 with that leftover leaves none for K. The hint of the no-guess page compares only numbers on the board, not leftovers, so it does not name this step.

When two numbers only overlap

Rule 2 needs all undecided cells of one number to lie among those of the other. In the middle of a straight border that does not happen: two numbers side by side share two of their three closed cells, and each has one of its own. The patterns 1-2-1 and 1-2-2-1 rely on a slightly stronger comparison.

Take a 1 that touches the closed cells a, b and c, and a 2 beside it that touches b, c and d. The shared cells b and c can hold at most one mine, because the 1 needs only one. The 2 needs two, so at least one of its mines lies outside the shared cells: d is a mine. This is the 1-2 pattern as most players use it: unlike the 1-1, it works anywhere along a straight border, not only at the edge.

In general: the extra cells of the second number hold at least what it still needs minus the most that the shared cells can hold. If that equals the number of extra cells, all of them are mines. The daily and no-guess boards of this site can always be finished without it; on other boards you may need it.

1-2-1

A 1, a 2 and a 1 side by side along a straight border of closed cells, with open cells behind them. The 2 touches the three closed cells in front of it; each 1 touches the cell in front of it, the one in front of the 2 and one more on the outside. Try the practice board before you read the reasoning.

Compare the left 1 with the 2. They share B and C, which hold at most one mine, so the third cell of the 2, D, is a mine. The same comparison from the right makes B a mine. The 2 now has both of its mines, so C is safe (rule 1), and each 1 has its mine, so A and E are safe (rule 1). In short: the mines are in front of the 1s, and the cell in front of the 2 is safe.

On the practice board the row of numbers lies on the bottom edge, and the cells at both ends of the row, F and G, are closed. They are safe for the same reason as A and E: each 1 already has its mine. The first two rules alone do not solve that board.

1-2-2-1

A 1, two 2s and a 1 side by side along a straight border of closed cells, with open cells behind them. Try the practice board first.

Compare the left 1 with the first 2. They share B and C, which hold at most one mine, so the third cell of the first 2, D, is a mine. From the right, the same comparison makes C a mine. Each 2 now touches both mines, so B and E are safe, and each 1 has its mine, so A and F are safe as well. In short: the mines are in front of the two 2s.

On the practice board, G and H at the ends of the row are safe as well: each 1 already has its mine.

Longer rows do not always resolve. In a 1-2-2-2-1, the same comparison from each end proves only the mine in front of the middle 2 and the safe cells at the outer ends; the other cells in front of the 2s stay undecided until another number helps.

Finding patterns in a game

• Read a flag as a mine already found. A 2 next to one flag still needs 1, and it plays the part of a 1 when the flag lies outside the cells of the pattern; the same goes for a 3 next to two flags.
• Check the cells, not only the digits. A pattern holds only when each number touches exactly the closed cells in the picture. One more closed cell, for example behind the row of numbers, can break it.
• Look along straight parts of the border first: the 1-1, 1-2, 1-2-1 and 1-2-2-1 all sit there.
• When no pattern fits, go back to the rules: count around one number, compare two numbers, count the remaining mines.

• Play the daily Minesweeper
• No-guess Minesweeper with rule hints

Common mistakes

• Trusting the whole 1-2-1 when a cell behind one of the 1s is still closed. That 1 may have its mine behind it, so the cell in front of it is no longer certain.
• Choosing between A and B in a 1-1 at the edge. The pattern proves only that C is safe; the mine can be in either cell until another number decides.
• Trusting a doubtful flag. Every pattern here assumes that your flags are right.