Minesweeper

Clear every square that does not hide a mine. Each number tells how many of the 8 squares around it contain mines. Use logic to find safe squares, flag the mines, and finish as fast as you can. Your first click is always safe.

How to play Minesweeper

1. Click (tap) a square to open it. The first click never hits a mine.
2. A number shows how many mines touch that square, including diagonals. A blank opens its neighbors automatically.
3. Right-click, long-press, or switch on Flag mode to mark a square you know is a mine.
4. Click an opened number whose mines are all flagged to open its other neighbors at once (chording).
5. You win when every safe square is open.

Logic patterns

• Count matches: if a 2 touches exactly two closed squares, both are mines.
• Satisfied numbers: if a 1 already touches a flag, every other neighbor is safe.
• 1-2-1 on a wall: the mines are under the 1s, and the square under the 2 is safe.
• 1-2-2-1: the mines are under the two 2s.

Probability in Minesweeper

When logic runs out, think in probabilities. On a fresh beginner board, 10 of 81 squares are mines, so a random square has a 10/81 ≈ 12% chance of a mine. Next to a 1 with 8 closed neighbors, each one has a 1/8 = 12.5% chance. Choose the square with the lowest chance, and prefer squares that will reveal the most information.

Minesweeper logic quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

How do I flag a mine on my phone?

Long-press the square, or turn on Flag mode so a tap places a flag.

Is the first click always safe?

Yes. Mines are placed after your first click, away from that square and its neighbors, so you always start with an opening.

Can Minesweeper always be solved with logic?

Not always. Some positions need a guess. Choosing the square with the lowest mine probability gives you the best chance.

What do the colors of the numbers mean?

They only make the numbers easier to tell apart: 1 is blue, 2 green, 3 red, and so on.

What is chording?

Clicking an opened number that already has the right number of flags around it, which opens all its other neighbors at once.

Sources

• Wolfram MathWorld: Minesweeper
• Kaye, R. (2000), Minesweeper is NP-complete, The Mathematical Intelligencer 22(2)

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