Unique Rectangle (Type 2) is very similar to Type 1, but instead of one corner having extra candidates, two corners (the "Roof") have the same extra candidate.
The Goal: Avoid the "Deadly Pattern" of 2 sets of identical pairs in a rectangle (2 rows, 2 cols, 2 boxes).
The Scenario
Imagine a "Floor" of two cells with pair {A, B}. Now imagine a "Roof" of two cells that should be {A, B} to form the deadly pattern, but they both have an extra candidate X.
- Floor (R7C3): {1, 4}
- Floor (R9C3): {1, 4}
- Roof (R7C9): {1, 4, 5}
- Roof (R9C9): {1, 4, 5}
The Logic
- The Premise: We know that we cannot have {1, 4} in all four cells (that would be a Deadly Pattern with 2 solutions).
- The Analysis:
- One of the Floor cells must be 1 or 4.
- One of the Roof cells must be 1 or 4.
- To avoid the pattern, at least one of the Roof cells must be the Extra Value (5).
- (If neither were 5, both would be {1, 4}, creating the deadly pattern).
- Therefore, either R7C9 is 5 OR R9C9 is 5.
- The Elimination:
- Since the 5 is proven to exist in one of the Roof cells, any cell that sees BOTH Roof cells cannot be a 5.
- We eliminate 5 from the intersection of the Roof cells' peers.
How to Spot It
- Find the Floor: Two cells in a row/col with identical pairs (e.g., {1, 4}).
- Find the Roof: Two other cells completing the rectangle.
- Check Candidates:
- Do the Roof cells contain the pair ({1, 4})?
- Do they both contain the same extra candidate (e.g., 5)?
- (They can have other extras, but they must share at least one common extra).
- Eliminate: Look for cells that see both Roof cells and remove the common extra candidate.
Comparison
- Unique Rectangle (Type 1): One corner has extras. Elimination is in that corner.
- Unique Rectangle (Type 2): Two corners have the same extra. Elimination is in the peers of the Roof.