Daily Challenges

T1–T5: The Trick Patterns

Trick patterns (T1 through T5) are advanced deductions that go beyond the standard 1-2-X and subset families. They require reasoning about multiple cells simultaneously — considering how two or more constraints interact in ways that aren’t obvious from any single number alone.

Also known as: Trick patterns, T-series. Numbered T1 (simplest) through T5 (most complex). These patterns are named for their “tricky” nature — they are correct deductions that most players miss.

These patterns are what separate expert-level solvers from intermediate players. When all the obvious patterns have been applied and the board seems stuck, trick patterns often unlock the next move.

T1 — The Double Constraint Trick

What It Looks Like

Two numbers share a pair of unrevealed cells, and a third number overlaps with one of those cells plus an additional cell. The shared pair creates a constraint that the third number can exploit.

How It Works

  1. Numbers A and B both touch cells X and Y. Together, these cells must contain a specific number of mines.
  2. Number C touches cell Y plus additional cells Z₁, Z₂…
  3. Knowing the constraint on X+Y from A and B tells you exactly how many mines must be in Y, which constrains C’s remaining cells.

When to Use It

When two numbers along a boundary share the same unknown pair, and a perpendicular number also touches one of those unknowns. Common at L-shaped boundaries.

T2 — The Exclusion Trick

What It Looks Like

A number’s constraint eliminates possibilities for an adjacent number, even though they don’t share enough cells for standard subset logic to apply.

How It Works

  1. Number A has N mines in M cells. You cannot determine which specific cells are mines.
  2. Number B touches some of A’s cells plus its own. B’s mine count, minus the maximum possible overlap with A’s mines, still forces mines into B’s non-shared cells.
  3. Conversely, B’s mine count minus the minimum overlap may prove some of B’s non-shared cells safe.

The Key Insight

Even without knowing exactly where A’s mines are, the range of possible overlaps (minimum to maximum) constrains B. When B’s required mine count outside the overlap exceeds the available cells, those cells must all be mines.

When to Use It

When basic subset logic shows no results, but two adjacent numbers have asymmetric overlap — one has many shared cells and the other has few.

T3 — The Bridging Trick

What It Looks Like

Two numbers that don’t share any cells are both constrained by a third number that overlaps both. The bridge number transfers information between the two endpoints.

How It Works

  1. Numbers A and C are far apart with no shared unrevealed cells.
  2. Number B (the bridge) shares cells with both A and C.
  3. A’s constraint fixes how many of B’s shared cells contain mines → this constrains B’s count for the cells it shares with C → which constrains C’s remaining cells.

Example

  • A = “1” touching cells {X, Y} (X shared with B)
  • B = “2” touching cells {X, Z, W} (X shared with A, Z shared with C)
  • C = “1” touching cells {Z, V}

A’s “1” means one mine in {X, Y}. If X has the mine, B needs only 1 more in {Z, W}. If Y has the mine, B needs 2 in {Z, W}, meaning both are mines. Either way, at least one mine is in {Z, W}, which constrains C through Z.

When to Use It

At boundaries where three or more numbers form a “relay chain.” Particularly common in the mid-game when two cleared regions are connected by a narrow isthmus.

T4 — The Parity Trick

What It Looks Like

The total mine count in a closed region must be a specific number, and the parity (odd or even) of that count forces at least one cell to be determined.

How It Works

  1. A region of unrevealed cells is fully surrounded by numbered cells.
  2. Adding all the constraints together, the total mine count for the region is known.
  3. If the total is the same as the number of cells, all cells are mines.
  4. If the total forces an odd/even split in a symmetric configuration, the asymmetric cell is determined.

The Parity Argument

When two cells are symmetric with respect to the constraints (either can be the mine), but the global mine count in the region forces an odd number of mines, the “extra” cell must be a mine. This is one of the few cases where the global mine counter (remaining mines on the entire board) provides local information.

When to Use It

Late-game positions where unrevealed regions are small and surrounded by numbers. Also useful when the remaining mine count from the counter constrains isolated cells.

T5 — The Mutual Exclusion Trick

What It Looks Like

Two cells cannot both be mines (or both be safe) because a number between them allows exactly one mine. Combined with another constraint, one specific cell is determined.

How It Works

  1. Number A touches cells X and Y among others, and after reduction, needs exactly 1 mine in {X, Y}.
  2. So X and Y are mutually exclusive — exactly one is a mine.
  3. Number B touches X (but not Y) plus other cells. Knowing that X is either mine or safe (with exactly one possibility) constrains B’s count for its other cells.
  4. If B needs N mines and has only N non-X cells, then X must be safe (B needs all its other cells to be mines, and if X were also a mine, B’s count would be exceeded).

The Mutual Exclusion Principle

Once you establish that exactly one of {X, Y} is a mine, you can substitute each possibility into neighboring constraints. If one possibility creates a contradiction, the other must be true.

When to Use It

When you’ve identified pairs of cells that are “either/or” (exactly one is a mine). Check whether either possibility contradicts any neighboring number’s constraint. This is essentially a focused, two-case backtracking search.

How to Practice Trick Patterns

  1. Master the basics first. T-patterns only help when 1-2-X, 1-1-X, subsets, and reduction have all been exhausted.
  2. Pause when you’re stuck. Instead of guessing, ask: “Are there two numbers that constrain each other indirectly?”
  3. Look for shared cells. Most trick patterns revolve around cells that two or more numbers share. Identify the shared cells first, then reason about the constraints.
  4. Use the mine counter. The global remaining mine count is especially useful for T4 parity arguments.
  5. Try both possibilities. For T5 mutual exclusion, literally try “what if X is a mine?” and “what if X is safe?” — if one leads to a contradiction, the other is true. This is valid logical deduction, not guessing.

Trick Patterns vs. Guessing

Trick patterns are logical deductions, not guesses. They may feel like guessing because you’re considering possibilities, but the key difference is:

  • Guessing: You click a cell without certainty, hoping it’s safe.
  • Trick pattern: You consider possibilities and prove that one leads to a contradiction, so the other must be true.

If both possibilities are consistent with the constraints and neither creates a contradiction, then it truly is a 50/50 — and no trick pattern can help. At that point you need probability estimation.