Minesweeper Patterns: 1-1, 1-2-1 and the Subtraction Method

Minesweeper Patterns: 1-1, 1-2-1 and the Subtraction Method

Created Aug 24, 2026

Most Minesweeper boards are not solved by intuition. They are solved by recognising a handful of number shapes that force a single answer, applying them, and repeating until the frontier moves. Once you can read those shapes on sight, the middle game stops being a series of small gambles and becomes bookkeeping.

This guide covers the patterns that actually resolve tiles on the board in Minesweeper, in the order they tend to appear. If you have never opened the game, start with the rules in how to play Minesweeper and come back here.

Every pattern reduces to two rules

Before memorising shapes, it is worth knowing what a shape is shorthand for. There are only two deductions in the entire game, and every named pattern is a situation where one of them fires:

  • Rule A โ€” all mines found. If a revealed number already has that many flagged neighbours, every remaining hidden neighbour is safe.
  • Rule B โ€” all remaining are mines. If a revealed number has exactly as many hidden neighbours as it still needs mines, every one of those hidden neighbours is a mine.

This is not a simplification invented for the guide. The solver built into Minesweeper โ€” the AI entry in the gear menu โ€” implements exactly these two tests and nothing else. It walks the list of revealed numbered tiles, counts hidden and flagged neighbours for each, and fires Rule B when the hidden count equals the outstanding mine count, or Rule A when the outstanding count reaches zero. When neither fires anywhere on the board, it picks a tile at random.

That tells you something useful about the game's difficulty curve: a position that the two rules cannot crack is genuinely stuck, not merely hard. Everything below is about spotting where the two rules apply faster than the solver does.

Read the number the right way

A number counts all mines touching that tile, including diagonals, and including the ones you have already flagged. The quantity you care about is never the printed number โ€” it is the number minus the flags you have already placed around it. Call that the outstanding count. Every pattern below is stated in outstanding counts.

Tiles on an edge have five neighbours instead of eight. Corner tiles have three. That shrinkage is why edges resolve first and why experienced players work the border before the middle.

The 1-1 pattern

Two adjacent tiles both showing an outstanding count of 1, sitting against a wall of hidden tiles. The left 1 touches hidden tiles A and B. The right 1 touches A, B and C.

The left 1 guarantees the single mine is in A or B. The right 1 needs one mine among A, B and C โ€” and A-or-B already supplies it. Therefore C is safe.

This is the most common resolution in the game and the one worth drilling first. The shape works in every orientation, and it works along the top and bottom edges of the grid as well as vertically down the sides. The tile it clears is always the one covered by the wider number and not by the narrower one.

A caution that costs people boards: the two 1s must be outstanding counts, not printed ones. If either tile already has a flag beside it, subtract that flag first. A printed 2 with one flag already placed behaves exactly like a 1 for the purpose of this shape, and treating it as a 2 produces a confident wrong answer. Every deduction in Minesweeper runs on the adjusted number.

The 1-2-1 pattern

Three tiles in a row reading 1, 2, 1, with three hidden tiles beneath them. The answer is fixed: the two outer hidden tiles are mines, and the middle hidden tile is safe.

The reasoning is short. The centre 2 needs two mines among the three hidden tiles. Each outer 1 touches only two of the three. If the middle hidden tile held a mine, both outer 1s would be satisfied by it, which would forbid mines in either outer position โ€” leaving the 2 with only one mine. Contradiction. So the middle is clear and the outer two carry the mines.

The pattern gives you three certain tiles at once, which is why it is the highest-value shape on the board. Look for it every time a row of numbers appears above an unbroken run of hidden tiles.

The 1-2-2-1 pattern

Four in a row reading 1, 2, 2, 1 above four hidden tiles. Here the two middle hidden tiles are mines and the two outer ones are safe โ€” the mirror image of the 1-2-1 result, which is exactly why the two get confused.

Work it from an end. The leading 1 sees hidden tiles A and B. The first 2 sees A, B and C. If both A and B were empty the 1 would be unsatisfied, so one of them holds a mine; the 2 then needs a second mine at C. Run the same argument from the other end and you get a mine at the mirrored position. Two mines placed, and the outer tiles are forced empty.

Confusing 1-2-1 with 1-2-2-1 is the single most expensive habit in the game. The tell is the length of the run: odd run, safe centre; even run, safe ends.

The subtraction method

When no named shape appears, the general tool is subtraction between overlapping numbers. Take two revealed numbers whose hidden neighbourhoods overlap. Subtract the smaller outstanding count from the larger, and subtract the shared hidden tiles from the larger tile's hidden set. Whatever remains on each side must account for the difference.

Concretely: a 3 touches hidden tiles A, B, C, D. A neighbouring 1 touches A, B only. The 1 claims one mine inside {A, B}. Remove that from the 3: two mines remain for {C, D} โ€” which is exactly two tiles, so both C and D are mines by Rule B.

Every named pattern is a memorised instance of this subtraction. Once subtraction is automatic you stop needing the names, and you start resolving shapes that have no name at all.

Corner and edge shapes

Corners resolve fastest because a corner tile touches only three others. A 1 in a corner with two revealed neighbours pins the mine on the third tile immediately. A 3 anywhere on the board with three hidden neighbours flags all three.

Along an edge, the useful shape is the 1-2 against the wall. A 2 on the border with exactly two hidden neighbours takes both. This happens constantly in the opening, and it is why clearing along the border generates far more forced moves per click than pushing into open middle ground.

The difficulty presets in Minesweeper change how often these shapes appear. The default 10×10 board carries ten mines, or 10% density, which leaves long stretches of open ground and plenty of clean 1-1 and 1-2-1 resolutions. The 16×30 expert board carries ninety-nine mines at 20.6%, where numbers crowd each other and subtraction between overlapping constraints does most of the work. Learn the shapes on the small board; they are the same shapes on the large one, just packed tighter.

Work the frontier, not the board

The frontier is the boundary between revealed numbers and hidden tiles. Every deduction you will ever make lives on it. Scanning the whole grid wastes time; scanning the frontier in one direction, resolving what fires, then scanning back the other way is how you keep the outstanding counts fresh.

A practical loop that works well in Minesweeper:

  1. Sweep the frontier for numbers whose outstanding count equals their hidden-neighbour count. Flag those. (Rule B.)
  2. Sweep again for numbers whose outstanding count is now zero. Clear their hidden neighbours. (Rule A.)
  3. Repeat until a full sweep produces nothing.
  4. Only then look for 1-1, 1-2-1 and subtraction opportunities across pairs.
  5. Only when that also produces nothing do you consider a guess.

Steps 1 and 2 cascade: every cleared tile adds a number that may unlock the next. Most of a board falls to those two steps alone.

When the patterns genuinely run out

Some positions are unsolvable by logic and require a guess. That is a property of the board, not a failure of technique โ€” and it happens more often on the 16×30 expert layout, where mines occupy 20.6% of the grid, than on the default 10×10 board at 10%.

When you are forced to guess, guess where the information is worst for the mines and best for you: prefer a tile touching the largest number of already-revealed numbers, because it is more constrained, and prefer opening new territory over nibbling at a settled frontier. There is also one opening square on this particular board that is never a mine at all, which is covered in how to play Minesweeper without guessing.

Before you commit to clearing a resolved area in bulk, read Minesweeper chording and flags โ€” the double-click shortcut in this version behaves very differently from the one you may be used to, and using it on an unflagged neighbourhood ends the game instantly.

Drill order

If you want the patterns to become automatic, practise them in this sequence on the default board: Rule B flagging, Rule A clearing, corner and edge resolutions, 1-1, 1-2-1, 1-2-2-1, then free-form subtraction. Each step builds on the previous one, and the last two are only worth drilling once the first four are instant.

The same deduction habits carry across the rest of the logic shelf. If you want more of it, Nonogram rewards the identical overlap-and-subtract reasoning on a larger grid, and the full set lives in the best puzzle games. Otherwise, open Minesweeper and start on the frontier.