Daily Challenges

The 1-2-X Rule: The Core Mine-Finding Pattern

The 1-2-X rule is the single most important building block in Minesweeper pattern recognition. Both the 1-2-1 and 1-2-2-1 patterns are just applications of this one rule. Master 1-2-X and you can derive complex patterns on the fly.

The rule: When a “1” and a “2” start from a wall edge, with unrevealed cells on one side, the cell beyond the “2” (the third unrevealed cell, marked X) is always a mine.

Also known as: 1-2 pattern, 1-2+ (extended form). The “+” variant applies the same logic when extra revealed cells are present beyond X.

How It Works

Three unrevealed cells (A, B, X) sit above a wall. Below them: a wall end, a “1”, and a “2”.

The “1” touches cells A and B → one mine is in {A, B}.

The “2” touches cells A, B, and X → two mines are in {A, B, X}.

Since {A, B} already contains one mine (from the “1”), X must contain the second mine needed by the “2”.

$$\text{mines in } {A, B, X} - \text{mines in } {A, B} = 2 - 1 = 1 \text{ mine in } {X}$$

X is a mine. Flag it.

Where to Apply 1-2-X

Starting from a Wall Edge

The classic case. The “1” must be at the edge of the wall (or the edge of known cells). This is what makes it work — the “1” fully constrains its two cells as a pair, giving you the subset for subtraction.

From Both Directions

You can apply 1-2-X from the left and from the right. This is exactly how the 1-2-1 pattern works — two 1-2-X applications from opposite ends.

After Reduction

A “2” next to a “3” with a flag touching the “3” reduces to 1-2-X. See Pattern Reduction.

What 1-2-X Does NOT Tell You

The 1-2-X rule tells you that X is a mine. It does not tell you which of A and B is the other mine — you only know that exactly one of them is. You need additional information (from other numbers or the mine counter) to determine which.

After flagging X, the “2” is reduced to effectively a “1” for cells A and B (since one of its mines is now flagged). This may help resolve A and B with information from neighboring numbers.

The Constraint Math

Given:

  • Constraint from “1”: $A + B = 1$
  • Constraint from “2”: $A + B + X = 2$

Subtracting: $X = 2 - 1 = 1$

X is a mine. The subtraction technique (comparing two constraints that share cells) is called constraint subtraction or subset logic, and it generalizes far beyond 1-2-X. See Subset Logic for the general version.

Common Variations

1-2-X Vertical

The pattern works vertically too — “1” and “2” stacked along the side of the board with unrevealed cells extending horizontally.

2-3-X (Reduced)

If both numbers have an adjacent flag, 2-3 reduces to 1-2. The “X” cell is still a mine.

1-2-X in Chains

After flagging X, the flag may satisfy another number, enabling a chord that reveals new cells, creating new patterns. This chaining effect is how experts clear boards quickly. See Combined Logic Chains.

Practice Tips

  1. Scan walls for “1” next to “2” — this is your primary trigger.
  2. Always start from the edge — the “1” must be at the end of the number sequence for 1-2-X to apply.
  3. Flag immediately — once you identify X, flag it. The flag often enables a chord on an adjacent number.
  4. Check both directions — after applying 1-2-X from one end, look at the other end. Another 1-2-X application in the other direction gives you the 1-2-1 or 1-2-2-1.