Minesweeper

The rules

Minesweeper hides a number of mines under a grid of covered squares. Click a square to open it. If it hides a mine, the game is over; if not, it shows a number: how many mines are in the eight squares touching it. Use those numbers to work out where the mines are, flag them if you like, and open every other square. You win when every safe square is open, and the clock stops.

An open square with no number has no mines around it, so the game opens all its neighbors for you, and their neighbors, until the opening is surrounded by numbers. That is what makes the first click open a whole area.

Board sizes and mine density

These are the sizes most minesweeper games use. What makes expert hard is not only its size but its density: about one square in 5 is a mine, against one in 8 on beginner.

Custom boards can be 5 to 40 squares each way, with at most (rows − 1) × (columns − 1) mines (64 on a 9 × 9, for example), so the first click always has room to open an area.

Reading the numbers: basic patterns

Most of the game is a handful of patterns along the edge of the opened area. In each diagram below, the top row is covered, the numbers sit on the edge of the opening, and everything under them is already open. A dot is an open square whose number doesn't change the answer. The solver in this game worked out every marked square.

1-1 against a wall

The first 1 touches only the first two covered squares, so its mine is one of those two. The second 1 touches those same two plus the third, and it already has its one mine among the first two, so the third square is safe. Whenever one number's squares are all inside another's and they need the same number of mines, the extra squares are safe.

1-2

The 2 needs two mines among its three covered squares. At most one of them can be in the two squares it shares with the 1, so the square beyond the 2 is a mine, and the 1 has its mine in the shared pair, so the square beyond the 1 is safe.

1-2-1

Two 1-2 patterns back to back: the mines sit next to the 1s and the square in the middle, next to the 2, is safe.

1-2-2-1

Again two 1-2 patterns, one from each end: the two mines sit next to the two 2s, and everything else along the edge is safe. Once you know these four shapes you will spot them everywhere, often bent around a corner.

Why the first click is safe

The board has no mines until you click. The game then places them at random everywhere except the square you clicked and the eight around it. Because none of your first square's neighbors is a mine, it shows no number and opens up an area, so you always have numbers to start from instead of a blind guess.

What "no guessing" means

A random board doesn't promise that logic is enough. Sometimes the last two squares in a corner touch exactly the same numbers and nothing can tell them apart, and the only way forward is a coin flip. With No guessing on, the game makes random boards after your first click and tests each one with its solver, which plays the board using only sure moves: single numbers, pairs of numbers like the patterns above, and the count of mines left. The first board it can clear completely is the one you get. If none turns up within a couple of seconds (very crowded custom boards), you get a normal board and a note saying so.

How often is a plain random board already solvable without a guess? We ran the solver on 1,000 random boards per level, with the first click in the middle:

So on expert, most random boards eventually ask for at least one guess, and no-guess mode is the way to make every loss your own mistake. No-guess best times are kept apart from normal ones.

Tips for faster games

• Chord instead of clicking one square at a time. Flag the mines around a number, then click the number to open all its other neighbors at once.
• Flags are optional. You win by opening every safe square; the mines never need flags. Some fast players never flag at all; others flag only where they are about to chord.
• Work the edges of the opening. Sure moves are almost always next to numbers. When you are stuck, look for a 1-2 or a 1-1 along the border.
• When you must guess, guess early and away from crowded numbers: a square far from the opening is often safer than a 50/50 in a corner, and you lose less time if it goes wrong.
• Use the hint to learn: it outlines a square you can be sure of, and tells you when there is none. Hinted games don't set best times.

Like logic puzzles? Try sudoku or printable sudoku, deal a game of solitaire, or make a word search. For word games there is the 5-letter word finder, the word unscrambler, the anagram solver, the crossword solver and the word finder.