Unique Rectangle Type 2: The Extra Candidate That Breaks the Deadly Pattern

The Symptom: A Deadly Pattern Almost Forms

You will notice a potential rectangle formed by four cells, each occupying the corners of two boxes, two rows, and two columns. Two opposite corners are bi-value cells containing only the same two candidates, for example, X and Y. The other two opposite corners are tri-value cells, also containing X and Y, but with an additional third candidate, Z. This is the hallmark symptom of a Type 2 Unique Rectangle.

The grid feels stuck because the bi-value cells (XY) and the tri-value cells (XYZ) create a fragile balance. If you ignore the extra candidate Z, the four cells could theoretically be filled as X and Y in two interchangeable ways, creating the deadly pattern that would break the puzzle's uniqueness. The presence of Z in two of the corners is the key that breaks this symmetry.

The Cause: Avoiding Multiple Solutions

The cause is the fundamental rule that a proper Sudoku must have a single solution. A true deadly pattern, where four cells in a rectangle contain only the same two digits X and Y, would allow those digits to be swapped, creating a second valid solution. Solvers use uniqueness techniques to logically avoid ever creating such a pattern.

In a Type 2 scenario, the deadly pattern is not yet present because two of the corners hold an extra option, Z. The logic dictates that to avoid the deadly pattern, at least one of these two corners must actually be the digit Z. If both of these corners were instead filled with either X or Y, the deadly pattern would be completed, violating the puzzle's uniqueness. Therefore, Z must be the solution in at least one of those two cells.

Diagnostic Check: Confirming the Pattern

First, identify the four cells forming the rectangle. Check that they lie in exactly two rows, two columns, and two 3x3 boxes. This alignment is non-negotiable for standard Unique Rectangle logic to apply.

Next, verify the candidate distribution. Two diagonally opposite cells must be pure bi-value cells with the same two candidates (XY). The other two diagonally opposite cells must be the tri-value cells, containing XY and one shared extra candidate (Z). All four cells must share the same base pair (X and Y). If the extra candidates differ between the two tri-value cells, it is not a standard Type 2. This pattern is a specific subset of Extended Unique Rectangles.

Applying the Fix: The Z Elimination

The deduction is direct: because at least one of the two tri-value corners must be Z, you can eliminate the candidate Z from any other cell that sees both of those corners. This is a powerful elimination that often reveals a Naked Single or other basic moves.

For example, if the two XYZ cells are in the same row, you cannot eliminate Z from that entire row, as each cell only sees itself. The power comes when a cell outside the rectangle is a peer to both XYZ cells. Since Z must be placed in one of them, that outside cell cannot possibly be Z. This elimination is the primary solving step provided by the pattern.

• Look for a cell that shares a row with one XYZ cell and a column with the other; it's a prime target for the Z elimination.
• After making the elimination, re-scan the affected units. A new single often appears immediately.

How It Differs from Type 1 and Other Types

It's easy to confuse rectangle types. In a Unique Rectangle Type 1, only one of the four corners has an extra candidate (XYZ), while the other three are clean bi-value cells (XY). The deduction there is that the extra corner must be Z, so X and Y can be removed as candidates from that cell.

Type 2 involves two corners with the extra candidate. The logic is different: we cannot pinpoint which of the two cells will be Z, only that one of them must be. This leads to the elimination of Z from common peers, rather than the elimination of X and Y from a single cell. Understanding this distinction is crucial for applying the correct logic.

When to Use This Technique and When to Get a Hint

Apply this technique in the mid-to-late game when the board has many bi-value and tri-value cells, and simpler methods like singles and pairs are exhausted. It is particularly useful in puzzles rated Hard or Expert. If you've identified the rectangle pattern but the deduction doesn't immediately create a new placement, stay patient. The elimination might be setting up a chain of simpler moves.

If you're stuck, even after looking for Unique Rectangles, use the Hint button. Our AI solver can confirm if a Type 2 pattern is present on your grid and show you the specific elimination, helping you internalize the pattern for next time. The provided puzzle grid is an excellent practice ground after you understand the theory.