Patterns

Basic Patterns

B1 - All neighbors are mines

When a number equals the count of all its hidden neighbors, every hidden neighbor is a mine.

B2 - All mines are accounted for

When the number of adjacent flags equals the cell's value, all remaining hidden neighbors are safe.

1–1 Pattern

When two 1s share all but one hidden neighbor, the unique neighbor of the second 1 is safe. The one mine for both 1s is within their shared neighbors.

The cell to the right of the second 1 (and beyond) is safe - the single mine must be in the shared cell to the left.

1–1+ (extended)

The 1–1 logic still applies even when cells are not directly touching, as long as you can show their hidden neighbor sets are identical except for one cell.

1–2 Pattern

A 1 next to a 2 at an edge. The 1 has one hidden neighbor that is also shared with the 2. The 2 needs one more mine in its unique neighbors - so that unique neighbor is a mine.

The second cell to the right of the 2 is safe; the first cell to the right of the 2 is a mine.

1–2+ (with extra shared cell)

If the 1 and 2 share two hidden neighbors and the 2 has one unique hidden neighbor, that unique neighbor is still a mine (the 2 needs one more mine than the 1 can account for).

1–2–1 Pattern

Three numbers in a row at an edge: 1, 2, 1. The central 2 needs exactly one mine in the two cells it doesn't share with the outer 1s. Each outer 1 already accounts for one mine in the shared region - so the cells "behind" the outer 1s are safe.

Both outer cells are safe. There is exactly one mine somewhere in the two cells directly above/below the 2.

1–2–2–1 Pattern

Four numbers in a row at an edge: 1, 2, 2, 1. The two outer cells behind the 1s are safe, and there is exactly one mine in each of the two inner pairs of cells.

Reduction Patterns

When one number's hidden neighborhood is a subset of another number's, you can subtract to get the mine count in the difference cells.

1–1 Reduction (1–1R)

Two cells with the same effective mine count share all but a few neighbors → those unique neighbors' mine count is zero → all are safe.

1–2 Reduction (1–2R)

A cell with value 1 is fully contained within a value-2 cell's neighborhood. The extra cell(s) of the 2 must contribute the remaining 1 mine → mine confirmed.

1–2–1 Reduction (1–2–1R)

Generalised: subtract the contribution of the outer 1s from the central 2. If the result is 0, all remaining cells of the 2 are safe. If it is 1, that single remaining cell is a mine.

Hole Patterns (H1, H2, H3)

A "hole" is an isolated hidden cell completely surrounded by revealed numbered cells. Because all constraints on it can be combined:

• H1 - If all surrounding numbers have already used up their mines, the isolated cell is safe.
• H2 - If the sum of remaining mines needed by surrounding numbers equals 1, the isolated cell is a mine.
• H3 - With two hidden cells in a cavity, you can often determine the exact configuration from the surrounding constraints.

Triangle Patterns (T1–T5)

Triangle patterns appear when cells share hidden neighbors in a triangular arrangement. Each variant (T1 through T5) covers a different configuration of 2–4 numbers with overlapping unknown regions.

T2–T5 follow the same principle with varying numbers of shared/unique cells. Always write out the constraint equations: number = mines in neighborhood.

High-Complexity Patterns

1–3–1 Corner

A 1–3–1 configuration pressed into a corner. The 3 sees three hidden cells; both 1s each share two of those cells with the 3. By subtraction, the cell unique to the 3 must be a mine, and the cells behind the 1s are safe.

2–2–2 Corner

Three 2s in an L-shape in a corner. All three see overlapping hidden regions. By combining constraints: the single inner corner cell is a mine; all others are safe.

1>2<1 Pattern

A 2 flanked by two 1s that share cells with it but not each other. Each 1 guarantees one mine in its exclusive sector of the 2's neighborhood. This means the 2's two mines are distributed - one per side - and the remaining cells are safe.

Dependency Chain

Sometimes no single pattern applies but a chain of deductions does. Start with cells that have the most constraints, apply each rule, and propagate newly revealed information to adjacent cells. Chains often unlock large portions of the board.

Last Turns

Mine Counting

At any point: remaining mines = total mines − flagged mines. If the remaining mine count equals the number of hidden cells, every hidden cell is a mine. If the remaining mine count is zero, every hidden cell is safe - reveal them all.

Combinations

When only a small number of hidden cells remain (e.g. 3 hidden, 1 mine), enumerate the possible mine positions and check which cells appear as mines in every possibility - those are definite mines. Cells that are safe in every possibility can be safely revealed.

Example: 3 hidden cells, 1 mine remaining, one of the cells is adjacent to a "1" whose only hidden neighbor is that cell → that cell is the mine; the other two are safe.

Practice

The fastest way to internalise these patterns is repetition in No-Guessing mode. Every board in NG mode is guaranteed fully solvable by logic alone - you'll encounter all the patterns above without ever needing to guess.