Back to strategy library
ExpertExpert / Master
Sudoku strategy guide

Unique rectangle: prevent a two-solution loop

A Type 1 unique rectangle has four cells in two rows, two columns, and two boxes. Three cells contain the same pair; the fourth contains that pair plus extras.

Key idea

If the fourth cell also took a pair digit, the rectangle could swap values and create two solutions. Its pair candidates must therefore be removed.

See the move, step by step

Inspect a 5/7 rectangle whose fourth corner also contains 9.

Step 1 of 4

Outline the four corners

Check two rows and two columns that cross exactly two boxes.

Rectangle rows

Step 2 of 4

Confirm three pure pair cells

Three corners contain only 5/7; R3C4 contains 5/7/9.

Rectangle unitsDeadly 5/7 pattern

Step 3 of 4

Protect uniqueness at the extra corner

Remove 5 and 7 from R3C4. Otherwise all four corners could become a swappable 5/7 loop.

Unique rectangleCandidates to remove

Step 4 of 4

Place the remaining value

R3C4 is left with 9, breaking the deadly rectangle.

RectangleConfirmed 9

Try it on today's puzzle

Use uniqueness techniques only on puzzles guaranteed to have one solution. Verify the four cells span exactly two boxes, not four.

Play today