Minesweeper patterns: proving 1–2–1 and checking a 50/50

Read the boundary before naming a pattern

For each clue, identify every adjacent hidden square, including diagonals. A board edge can remove neighbours; a position in the middle may have extra ones. Missing even one square can invalidate a familiar-looking move.

Minesweeper Online illustrates patterns including 1–2–1 and reductions of larger clues. ¹ Treat each diagram as a set of conditions to verify. Matching the visible digits is not enough when the hidden neighbours differ.

Subtract proven mines, not hopeful flags

A clue of 3 with two proven neighbouring mines still requires one mine among its other hidden neighbours. Its remaining requirement is therefore 1. A flag is only a mark you placed: an uncertain guess does not become evidence because it has a flag.

For example, suppose a 2 has hidden neighbours X and Y, plus one proven mine. Write X+Y=1, where a variable is 1 for a mine and 0 for a safe square. This translation makes constraints easier to compare, even when the original printed digits look unfamiliar.

Why the middle of this 1–2–1 is safe

Call three unknown squares A, B and C. After accounting for every other neighbour, the left clue requires A+B=1, the middle requires A+B+C=2, and the right requires B+C=1. These are exact conditions: there are no additional unknown neighbours of those clues.

Subtract the first equation from the middle one: C=1. Substitute into the right: B+1=1, so B=0. The left then gives A=1. Both outer squares are mines, and the middle square is safe. This conclusion follows from the neighbour sets, rather than the appearance of the digits.

Check it backwards: 1+0=1, 1+0+1=2, and 0+1=1. If another hidden square D touches a clue, its equation changes. Do not carry the old result across automatically; rewrite the complete constraints first.

Look for one set inside another

Suppose one clue gives X+Y=1 and another gives X+Y+Z=1. Subtraction proves Z=0. If the second equation instead equals 2, Z=1. You still do not know whether X or Y contains the mine, but that uncertainty does not prevent a conclusion about Z.

You do not need to solve an entire region before acting. A square is safe when it is safe in every valid arrangement. Opening it may expose another clue that resolves the uncertain pair on the next turn.

Use the remaining mine count carefully

A locally valid arrangement can fail the whole board. Imagine three mines remain. One region contains exactly two, and a separate pair contains exactly one. If these counts are proven, the regions do not overlap and you have checked the full board, any other hidden squares are safe: the entire mine budget is accounted for.

Do not add adjacent clue totals blindly; the same mine can contribute to several clues. Also distinguish a counter reduced by your flags from a proven remaining total. A mistaken flag can damage global counting just as easily as local subtraction.

When is a 50/50 genuinely unresolved?

Two squares sharing one mine are not automatically a final dead end. Check other clues, the continuing boundary and the total mine count. One choice may force an extra mine elsewhere and become impossible. Look for that contradiction before calling the position a guess.

A truly symmetric choice remains when all constraints permit two equivalent placements: the mine is on the left or on the right, and no available information distinguishes them. With equally likely generation of those alternatives, either square has a one-half survival chance. No universal trick supplies missing information. Any no-guess guarantee depends on the specific game mode and generator.

Train explanations rather than recognition

Before a move, state the reason: “this pair contains one mine; the larger set also contains one; therefore the extra square is safe”. If the explanation is only “it looks like a pattern”, check the neighbours again. After a mistake, reconstruct the missing condition instead of immediately starting another board.

Try changing the worked A,B,C example by adding an unknown D beside the left clue. Which equations survive, and which conclusions no longer follow? Small variations teach the boundary of a pattern, a skill you can use on positions you have never seen.