Mines strategy: reading the numbers together

Play Mines

One number on its own only gets you so far. Most of the game is reading two or three numbers together, and when you're stuck, the answer is usually in two numbers sitting side by side.

How the difficulty works

Bigger boards have more mines, but size isn't what makes Hard hard. Each tier is set by the trickiest deduction you'll need:

Easy (9×9, 10 mines) mostly needs one number at a time, with the odd comparison of two.
Medium (10×14, 24 mines) always needs at least one subset: comparing two numbers whose covered cells nest.
Hard (12×16, 38 mines) needs an overlap between two numbers, or counting the mines that are left.

One number at a time

The foundation, covered in how to play: a number that has as many covered neighbours as it needs mines is surrounded by mines; a number whose mines are all flagged has only safe neighbours left.

The outlined number can only be satisfied one way, so the tinted cell is a mine. From Easy puzzle #1 — play it

It helps to think of each number as what it still needs, not what it shows. A 3 with two flags next to it is really a 1. Read that way, many cluttered corners suddenly look simple. Flag as you go, so you don't have to keep the count in your head.

Comparing two numbers: subsets

When no single number tells you anything, look for two neighbouring numbers where every covered cell of one also touches the other. Whatever the first needs is somewhere in the shared cells, so the rest of the second's covered cells hold the difference.

The lower 3 still needs one mine among its two covered cells, and every one of those also touches the upper 2. The upper 2 needs two mines, so the one cell only it touches must hold one mine: that cell, outlined with dashes, is a mine. From Medium puzzle #1 — play it

The most common case is a 1 next to a 1 along an edge of the opened area. The first 1 has two covered cells, the second has those two and one more. The first 1's mine is in the shared pair, which satisfies the second 1 too — so its extra cell is safe. Learn to spot this one at a glance and you'll clear Medium boards far faster.

The 1-2-1 and 1-2-2-1 patterns

Two shapes come up so often along straight edges that they're worth memorising. Where the numbers 1, 2, 1 run in a line against a straight edge of covered cells, the mines are under the two 1s and the cell under the 2 is safe. Where 1, 2, 2, 1 run in a line, the mines are under the two 2s and the cells under the 1s are safe. Both are just subsets applied a couple of times, so work them through once to see why, then trust them.

Hard: overlaps

Sometimes two numbers share some covered cells but each also has cells of its own. Then ask: how many mines can the shared cells possibly hold? No more than the smaller number needs. If the bigger number needs more than that, the excess has to sit in its own cells — and if it has exactly that many cells of its own, they're all mines.

The upper 2 needs one mine and the lower 3 needs two mines. They share two covered cells, which can hold at most one mine — the upper 2's limit. So the lower 3's one cell of its own must hold the other one mine (outlined with dashes). Now the upper 2's mine is in the shared cells, and the cells only it touches, ringed, are safe. From Hard puzzle #1 — play it

Overlaps are the subset idea with one more step, and they're the move most players miss. When you're stuck on a Hard board, go round the edge of the opened area pair by pair and ask the overlap question for each.

Hard: counting the mines

The counter above the board tells you how many mines are still unflagged. Near the end of a game, it can settle what the numbers can't. If every mine has been found, every covered cell left is safe, however cut off it is. If the mines left equal the covered cells left, they're all mines.

All 38 mines are flagged, so the last two covered cells, ringed, are safe — even though no number next to them could prove it. From Hard puzzle #12 — play it

The count can help earlier too, when only a few mines are left and you can see they must all be in one region.

Good habits

Work along the edge. All the information is on the border between opened and covered cells. Cells deep in the covered area tell you nothing until the edge reaches them.
Flag what you know. It's optional, but flags turn every number into "what it still needs" without mental arithmetic, and they let you open a number's other neighbours with one tap.
Easy first. After each move, look for new single-number deductions before reaching for comparisons. A newly opened cell often unlocks its neighbours straight away.
Stuck? Pair up. Take every pair of touching numbers on the edge and ask the subset question, then the overlap question. On these boards, one of them will always give.
Hint names the numbers. If you'd rather not search, it outlines the numbers that settle something and tells you what they settle.