##### Minesweeper Patterns

A pattern is a common arrangement of numbers with only one solution. Learning patterns is important because thinking wastes time.

The two most famous patterns are 1-2-1 and 1-2-2-1. You should memorise these immediately.

The 1-2-1 pattern has one solution.

The 1-2-2-1 pattern has one solution.

##### Advanced Patterns

The 1-2-1 and 1-2-2-1 patterns are actually combinations of a more important pattern. When you see 1-2-X on a row the X is always a mine.

Take some time to understand how this pattern works. There are two mines in three squares (because the 2 touches three squares) but there is one mine in the first two squares (because the 1 touches two of the three squares). The third square must contain the other mine.

The 1-2-1 pattern has one solution.

Apply the 1-2-X pattern from the left.

Apply the 1-2-X pattern from the right.

The 1-2-2-1 pattern has one solution.

Apply the 1-2-X pattern from the left.

Apply the 1-2-X pattern from the right.

The other important pattern is 1-1-X on a row starting from a border. The first 1 touches two squares and the second 1 touches three squares. Both clues are true so the third square must be empty. This logic is the opposite of the 1-2-X pattern (which always has a mine in the third square).

The pink 1 means there is one mine in the three squares it touches. The yellow 1 means the mine is in the subset of two yellow squares. The third square from the border must be empty.

The pink 1 means there is one mine in the three squares it touches. The yellow 1 means the mine is in the subset of two yellow squares. The third square from the border must be empty.

The 1-1-X pattern can also wrap around corners...

The pink 1 means there is one mine in the five squares it touches. The yellow 1 means the mine is in the subset of two yellow squares. The pink squares must be empty.

Each pink 1 means there is one mine in the five squares it touches. Each yellow 1 means the mine is in the subset of two yellow squares. The pink squares must be empty.

##### Advanced Logic

Sometimes a mine is in a subset of squares so the remaining squares must be safe. This is how the 1-1-X pattern works.

The pink 1 means there is one mine in the three squares it touches. The yellow 1 means the mine is in the subset of two yellow squares. The third square from the border must be empty.

The pink 1 means there is one mine in the three squares it touches. The yellow 1 means the mine is in the subset of two yellow squares. The third square from the border must be empty.

The pink 2 touches four squares and the yellow 2 touches a subset of two squares. The mines must be in the yellow squares so the pink squares are safe.

The pink 2 touches four squares and the yellow 4 (effectively a 1) touches a subset of two squares. The mine must be in the yellow squares so the pink squares are safe.

Sometimes it is better to find mines instead of only looking for safe squares.

The 3 touches four squares. The yellow 1 touches a subset of two squares. The second and third mines must be in the pink squares.

The 4 touches five squares. The yellow 1 touches a subset of two squares. The second, third and fourth mines must be in the pink squares.

The 3 touches five squares. Each yellow 1 touches a subset of two squares. The third mine must be in the pink square.

The pink 4 touches five unopened squares. One is flagged so there are three mines left in four squares. The yellow 2 touches a flag so there is one mine left in two yellow squares. The two pink squares must be mines.

You can combine patterns and logic to form chains of logic alternating between finding mines, using 1-1-X and using subsets. One of the earliest Minesweeper games was called Relentless Logic!

Find the two mines and use 1-1-X to open the third square then open the pink squares.

Find the three mines and use 1-1-X to open the third square then open the pink squares.

Find the mine and use 1-1-X to open the third square then open the pink squares.

Find three mines. The 4 effectively becomes 1 and the 2 effectively becomes 1. Use 1-1-X to open the third square then open the pink squares.

##### Pattern Reduction

Complex mine arrangements can be reduced to patterns.

You simply subtract the known mines from each number. For example, if you flag a mine touching a 3 it becomes a 2.

The next examples are more complicated because you need to solve the entire situation in your head to see the pattern. If you do not see the patterns take turns reducing numbers and using 1-2-X to solve these examples.

1-2-1

1-2-2-1

1-2-2-1 and 1-2-1

1-2-1 and 1-2-1