Mine Finder Patterns: 1-2-1, 1-2-2-1 and How to Guess Well
Why patterns matter
A classic mine-sweeping puzzle looks like a game of luck the first time you play it. It isn’t. Almost every position can be read with a handful of small logical patterns, and once you recognize them you stop thinking square by square and start seeing whole sections of the board at a glance.
This guide covers the patterns we lean on most when playing our own Mine Finder. Everything here works on any board size. In the diagrams below, # is a covered square, F is a flag, . is an uncovered blank, and numbers are uncovered numbers. Rows are written top to bottom.
The two basic rules
Every pattern in this article is built from two facts.
Rule 1: all mines found. If a number already has that many flags around it, every other covered neighbor is safe.
Rule 2: all squares are mines. If a number has exactly as many covered neighbors as its value, every one of them is a mine.
A 1 touching a single covered square is Rule 2. A 3 touching three flags and one covered square is Rule 1. These alone clear most of an Easy board. The patterns below are what you use when neither rule applies directly.
Subtraction: the idea behind every pattern
Take two numbers that sit next to each other. If all the covered squares one of them can see are also seen by the other, you can subtract.
Say a 1 can see two covered squares, and a 2 right beside it can see those same two plus a third. The two shared squares contain exactly one mine, because that’s all the 1 allows. The 2 needs two mines. So the third square, the one only the 2 can see, must hold the other mine.
In general: (bigger number) minus (smaller number) = mines in the squares only the bigger one can see. If that difference equals the number of those squares, they’re all mines. If it’s zero, they’re all safe. The famous named patterns are just this subtraction applied to common shapes.
The 1-2-1
This shows up constantly along the straight edge of an opened area:
# A B C #
? 1 2 1 ?The covered squares above the 1, the 2 and the 1 are labeled A, B and C. A ? is whatever continues the edge; it doesn’t change the logic.
- The 2 needs two mines among A, B and C.
- Suppose B is a mine. Then the left 1 is satisfied by B, so A is safe. The right 1 is satisfied by B too, so C is safe. That leaves the 2 with only one mine. Contradiction.
- So B is safe, and the 2’s two mines must be A and C.
Result: the squares above both 1s are mines, the square above the 2 is safe. Once you’ve flagged A and C, both 1s are satisfied, so any other covered squares they touch are safe too.
The 1-2-2-1
The longer cousin:
# A B C D #
? 1 2 2 1 ?The covered squares above the four numbers are A, B, C and D.
- The left 2 sees A, B and C. The left 1 sees A and B (plus the square to the left of A) and allows only one mine among them. So the left 2 gets at most one mine from A and B, and its second mine must be C.
- By the same argument from the right side, B must be a mine.
- With B and C flagged, both 1s are satisfied, so A and D are safe.
Result: mines above the two 2s, safe above the two 1s. A handy way to remember both patterns: in 1-2-1 the mines sit under the 1s; in 1-2-2-1 they sit under the 2s.
Walls and corners
The edge of the board is your friend, because numbers there can see fewer squares.
1-1 against a wall
|# # #
|1 1 ?The 1 against the wall sees only two covered squares: the one above it and the one diagonally right. The second 1 sees those same two, plus the next square to the right. The first two already contain the one mine, so the third square is safe. This is subtraction with a difference of zero.
1-2 against a wall
|# # #
|1 2 ?Same shape, but now the second number is 2. The first two squares hold one mine, so the third square must hold the other. The third square is a mine.
Corner 1
A 1 tucked into a corner with a single covered neighbor is a guaranteed mine by Rule 2. Corners are also where zero squares are most common, because a corner square has only three neighbors instead of eight.
Reading the whole board
Patterns handle local shapes. When they run out, zoom out.
Count remaining mines. The counter at the top of Mine Finder shows mines minus flags. Near the end of a game, compare that to the number of covered squares that aren’t touching any number. If the numbers on the edge of the opened area account for every remaining mine, the isolated covered squares elsewhere are all safe.
Look for shared squares. Two numbers several squares apart can still overlap if they reach into the same pocket of covered squares. Scanning for overlaps is slower than spotting a 1-2-1, but it’s how the hardest positions get solved.
Chord to save time. Once a number’s mines are flagged, tapping it opens all its other neighbors at once. Good players flag only the mines they need for chording and leave the rest.
When you really must guess
On a purely random board, some positions have no logical answer. The classic example is two covered squares with one mine between them and nothing else that can tell them apart. You’ll have to pick. Here’s how to pick well.
Guess as early as possible
If you spot a true 50/50, take it now rather than solving the rest of the board first. If you’re going to lose, it’s better to lose in the first minute than the tenth.
Compare the local odds with the global odds
A 1 touching three covered squares puts roughly a one-in-three chance on each of them. Meanwhile, a covered square far from any number has odds close to the overall density: remaining mines divided by remaining covered squares. On Hard at the start that’s around 20%, which is lower than one in three. A square away from the numbers can be the safer bet.
Prefer squares that will teach you something
A safe square that’s surrounded by covered squares might open a whole new area or give you a number that settles the region. A safe square wedged between known numbers might tell you nothing new. When two guesses have similar odds, choose the one that gives more information.
Corners and edges open more often
Squares with fewer neighbors are more likely to be zeros, and a zero opens a patch for free. When guessing blind, a corner is a reasonable choice.
Or skip the guessing entirely
This is exactly why we built a no-guess mode into Mine Finder, and it’s on by default. Before a board is shown to you, our solver plays it from your first click using the same rules described above: the two basic rules, subtraction between overlapping numbers, and mine counting at the end. If it gets stuck, the board is discarded and a new one is generated. Every board you see can be finished with logic alone.
That changes how you play. When you feel stuck on a no-guess board, it means there’s a pattern you haven’t spotted yet, usually a subtraction between two numbers that share covered squares. Go back to the edge of the opened area and check each pair of neighboring numbers. The answer is always there.
If you’d rather have the classic experience, flip the setting off in the footer and practice your guessing technique on fully random boards. Either way, start a game of Mine Finder and try spotting a 1-2-1 in the first ten seconds.
