Daily Challenges

The T-Pattern: Solving at T-Shaped Junctions

The T-pattern appears when two boundary lines meet at a perpendicular junction, forming a T-shape in the unrevealed area. The numbers at the junction constrain each other from multiple directions, creating deductions that aren’t possible along a simple straight wall.

Also known as: T-junction pattern, perpendicular boundary pattern. This pattern exploits the extra constraints created when boundary lines intersect.

What Makes a T-Pattern

The Shape

A T-pattern forms when:

  1. A row of numbers runs along one wall (the top of the T).
  2. A perpendicular column of numbers extends from the middle (the stem of the T).
  3. Unrevealed cells fill the regions between these boundaries.
    W  W  W  W  W
    W  1  2  1  W
    ?  ?  ?  ?  ?
    ?  ?  1  ?  ?
    ?  ?  ?  ?  ?

The top row (1-2-1) is the cap of the T. The “1” below is the beginning of the stem.

Why T-Junctions Are Special

Along a straight wall, each number constrains cells on one side. At a T-junction, the stem number constrains cells that the cap numbers also constrain, but from a perpendicular angle. This creates overlapping constraint regions that make subset logic much more powerful.

Common T-Pattern Configurations

1-2-1 Cap with Stem

The classic 1-2-1 along the top of the T resolves mines at the ends and safe in the middle. The stem number then applies independently to the perpendicular cells. This often cascades into solving the entire junction.

1-1 Stem Extending from a Wall

Two “1"s running perpendicular to a wall edge create a 1-1-X configuration in the perpendicular direction. The cell at the far end of the stem is safe.

High-Number Junction

When the junction cell is a “3” or “4”, it touches cells from both the cap and the stem regions. Combined with the constraints from the cap numbers, the junction cell often fully resolves — every neighbor is either determined safe or mine.

Solving Strategy for T-Patterns

Step 1: Solve the Cap First

The cap of the T (the straight wall portion) usually contains recognizable patterns: 1-2-X, 1-1-X, 1-2-1. Solve these first to flag mines and mark safe cells.

Step 2: Reduce the Junction Number

After solving the cap, any flags placed reduce the junction number. A “3” that gained two flags from the cap becomes an effective “1” — which then constrains the stem.

Step 3: Solve the Stem

With the junction number reduced, apply standard wall patterns along the stem. The stem often starts with an effective 1-1 or 1-2 from the junction, leading to 1-1-X or 1-2-X deductions.

Step 4: Check for Side Constraints

Numbers in the cap that are adjacent to the stem may have their constraints partially satisfied by stem flags. Reduce them and check for additional patterns.

T-Patterns in Practice

T-patterns appear constantly in mid-game and late-game Minesweeper. Whenever two cleared regions are separated by a thin strip of unrevealed cells, the boundary between them often forms T-junctions. These junctions are high-value targets because:

  • Double constraints — cells are constrained from two perpendicular directions.
  • Cascade potential — solving the junction often clears the entire connecting strip.
  • Reduction opportunities — the junction cell typically has high numbers that reduce dramatically once the cap is solved.

Common Mistakes

Solving Cap and Stem Independently

The power of the T-pattern is in how the cap and stem interact. Solving the cap without checking how the results affect the stem misses deductions. Always re-evaluate the junction and stem after each cap solve.

Ignoring Diagonal Neighbors

At a T-junction, the junction cell often has diagonal neighbors that are constrained by both the cap and stem logic. These diagonals are easy to overlook but are frequently the key cells that complete the deduction.

Overcomplicating the Analysis

Many T-patterns reduce to simple 1-2-X or 1-1-X once you solve the cap. Don’t try to analyze the entire T at once — break it into cap → junction → stem and solve sequentially.