Unique Rectangle
advancedAvoiding deadly patterns that would create multiple solutions
Unique Rectangle (UR) techniques exploit the fact that a valid Sudoku has exactly one solution. If a pattern of four cells would create an ambiguity, we can use that knowledge to make eliminations.
Understanding the Concept
A "deadly pattern" is a rectangle of four cells spanning exactly two rows, two columns, and two boxes, where all four cells contain the same two candidates {A,B}.
If this pattern existed, you could swap A and B in all four cells and still have a valid solution — meaning multiple solutions, which is not allowed.
Therefore, at least one corner must have candidates beyond {A,B}, preventing the deadly swap.
Type 1: Three corners have only {A,B}, and one corner has {A,B,...extra}. Remove A and B from the fourth corner — the extra candidates must be the answer there.
Type 2: Two corners in the same house have {A,B,C}. Digit C must go in one of them. Eliminate C from other cells in their shared house.
Type 4: Two corners have extra candidates. If one extra is confined, you can eliminate the UR digits from those corners.
This technique relies on uniqueness — only use it when the puzzle is guaranteed to have one solution.
Examples
Unique Rectangle Type 1
Cells R1C3, R1C7, R6C3, R6C7 form a rectangle spanning two boxes. Three corners have only {1,8}: R1C3, R1C7, R6C3. The fourth corner R6C7 has {1,6,8}. To avoid the deadly pattern, R6C7 cannot be just {1,8}. Therefore, remove 1 and 8 from R6C7 — it must be 6.
Pro Tips
- •Look for rectangles where two candidate digits appear in four cells spanning two boxes
- •Three corners with only those two candidates is the classic Type 1 setup
- •The fourth corner MUST use its extra candidates — otherwise multiple solutions would exist
- •Only use Unique Rectangle if the puzzle is guaranteed to have a unique solution
- •This technique is considered meta-logic — it reasons about uniqueness, not pure Sudoku constraints
