Daily Challenges

The 2-2-2 Corner Pattern: Full Mine Saturation

The 2-2-2 corner pattern occurs when three “2"s run along a wall that turns a corner. The corner geometry reduces the number of unrevealed neighbors so severely that every unrevealed cell adjacent to the “2"s must be a mine. Flag them all.

Also known as: 2-2-2 corner. A saturated corner configuration where the mine count equals the number of available cells.

How the 2-2-2 Corner Works

The Setup

Three “2"s wrap around a wall corner:

    W  W  ?  ?
    W  2  ?  ?
    ?  2  ?  ?
    ?  2  W  W
    ?  ?  W  W

The Logic

  1. The corner “2” has limited unrevealed neighbors due to the wall bend — typically 3 cells.
  2. Each adjacent “2” shares some of those cells and adds a few of its own.
  3. Count total unrevealed cells across all three “2"s. In the corner configuration, the total number of distinct unrevealed cells equals or nearly equals the total mine count required.
  4. When the unrevealed cell count matches the constraint sum, every cell is a mine. Flag them all immediately.

Why Three “2"s Are Special at Corners

On a straight wall, three “2"s in a row could be a 1-2-2-1 in disguise (after reduction) — with safe cells in the middle. But at a corner, the wall bend reduces the available cells on the outside of the bend. Fewer cells + same mine requirements = full saturation.

Step-by-Step Example

  1. Identify the corner “2.” It sits where the wall changes direction.
  2. Count its unrevealed neighbors: At a corner, a “2” typically has 3 unrevealed neighbors, and it needs 2 mines. That leaves only 1 safe cell.
  3. Look at the flanking “2"s. Each shares neighbors with the corner “2” and adds new ones. When all three “2"s are considered together, the total mine count (6) closely matches the total unrevealed cells.
  4. Apply subset and overlap logic. The shared cells between adjacent “2"s constrain the solution further. In most 2-2-2 corner configurations, every unrevealed cell resolves to a mine.

Variations

2-2-2 With One Flag Already Placed

If one “2” already has a flag neighbor, it effectively becomes a “1”. The pattern still resolves — the reduction makes the remaining cells even more constrained.

2-3-2 Corner

A “3” in the middle at a corner is even more constrained. The “3” needs 3 mines in its limited corner neighborhood — almost always saturating the available cells.

1-2-2 Corner

If one end is a “1” instead of “2”, the side near the “1” has a safe cell. Apply 1-2-X from the “1” end to find it.

How to Spot It

  1. Scan corners for clusters of “2"s. Multiple “2"s near a wall corner is a strong signal.
  2. Count unrevealed cells. If the mine count required (sum of the numbers, adjusted for overlap) equals the unrevealed cell count, everything is a mine.
  3. Flag aggressively. Saturated corners are one of the few situations where you should flag every cell without hesitation.

Common Mistakes

Applying Straight-Wall Logic to Corners

On a straight wall, 2-2-2 often has safe cells (it might be a reduced 1-2-2-1). At a corner, the reduced cell count changes the outcome. Always count actual unrevealed neighbors, don’t assume straight-wall patterns.

Not Following Through After Flagging

Flagging all the mines in a 2-2-2 corner often satisfies multiple numbers, enabling chords that cascade into solving large adjacent regions. Don’t just flag and move on — chord the satisfied numbers.