AI MINESWEEPER
Minesweeper Patterns Explained: 1-1, 1-2, 1-2-1 and 1-2-2-1
Ask a strong Minesweeper player how they cleared a wall of numbers without stopping and they'll say "it was a 1-2-1." Patterns are the vocabulary of the game — board shapes whose solution is always the same, recognized in a glance instead of re-derived every time. Here are the four that matter most, each with a diagram, plus the single logical rule that generates every one of them.
The One Rule Behind Every Pattern
Every revealed number is a little equation: "exactly N mines among these hidden neighbors." Patterns appear when two equations overlap:
If number A's cells are a subset of number B's cells, subtract: the cells only in B must contain exactly B − A mines. If that difference is 0, those cells are all safe; if it equals the count of those cells, they're all mines.
That's it. The named patterns below are just the subset rule applied to the shapes that come up constantly. (It's also literally rule 3 inside our AI hint engine — when the hint says a cell is safe "by comparing two numbers," this is what it did.)
1-1: the Free Cell
1-1 from the left edge: the cell over the gap (marked ✓) is safe.
Two 1s side by side, with the hidden row above them, starting from an edge (or from a revealed/settled column). The left 1 sees cells {a, b}; the right 1 sees {a, b, c}. Subset rule: c must hold 1 − 1 = 0 mines — it's free. Whenever a 1-1 runs from a border, the third cell over is openable. This is the pattern that unsticks more beginner games than any other.
1-2: the Forced Mine
1-2 from the left edge: the cell only the 2 sees is a mine.
Same shape, but the second number is a 2. The 1 sees {a, b}; the 2 sees {a, b, c}. Subtract: c holds 2 − 1 = 1 mine across exactly one cell — c is a mine, flag it without knowing anything about a or b. Read it left-to-right as a rhythm: one-two, mine on the far side of the two.
1-2-1: the Classic
1-2-1: mines sit above the 1s, and the cell above the 2 is safe.
The most famous shape in the game. Apply the subset rule twice — once from the left 1 into the 2, once from the right 1 into the 2 — and the only arrangement consistent with both is mines above the two 1s, safe above the 2. You'll meet 1-2-1 constantly along straight walls — solve it on sight and the wall collapses.
1-2-2-1: the Long Wall
1-2-2-1: the mines are above the 2s; the cells above the 1s are safe.
The 1-2-1's big sibling, and delightfully counter-intuitive: the mines sit above the 2s, and the cells above the 1s are safe. Derive it once with the subset rule (each outer 1 caps its side at one mine; the inner 2s then need both their exclusive cells), then never derive it again — just recognize the rhythm.
1-1-1, 1-1-2 and Longer Runs
The four shapes above cover most boards, but the same subset rule keeps working for longer runs of numbers along a wall — and these are the patterns people look up by name once they meet them.
1-1-1 is just the 1-1 free cell repeated: in an unbroken run of 1s along an edge, every third cell is safe. Clear the free cell the first 1-1 hands you, slide one step along, and the next 1-1 gives you another — so a long wall of 1s opens up in a steady rhythm rather than all at once.
1-1-2 is where a run of 1s meets a 2, and the 2 does the deciding. Reading into it, the cell under the second 1 and the cell just past the 2 are both mines, while the cell under the first 1 and the cell under the 2 itself are safe. It falls straight out of the subset rule: the 2 needs two mines, the 1-1 before it has already freed the cell they share, so both mines are forced to the outside.
That is why it pays to learn the rule rather than memorise a chart: 1-1, 1-2, 1-2-1, 1-2-2-1, 1-1-1, 1-1-2 and every other named run are the same subtraction applied one number at a time. Name any of them and you are really naming one move you already know.
Edges Change Everything
All four patterns assume the row of numbers is "sealed" from the sides — by the board edge, or by cells already revealed or flagged. In the open field a stray extra neighbor breaks the subset relationship, and the "pattern" stops being one. That's the most common way players go wrong: applying 1-2-1 in the middle of an unsealed wall. When in doubt, fall back to the subset rule itself — count the actual overlapping cells rather than trusting the shape.
Practice Where Patterns Are Guaranteed to Work
Our AI Minesweeper is a pattern gym: in No-Guess mode every board is verified solvable by pure logic, so whenever you stall, there is a pattern on screen you haven't spotted. Stuck anyway? The 💡 hint doesn't just point — it names the reasoning ("comparing the constraints of two overlapping numbers"), which is exactly how these shapes are built. A few boards of that feedback loop and you'll read 1-2-1 walls the way you read words.