Unique Rectangle Type 3
This deduction assumes the puzzle has exactly one solution and that all earlier candidate removals were sound. A Type 3 Unique Rectangle starts from a candidate state in which swapping two digits across the construction would preserve every touched row, column and box. The rescue alternatives act as one virtual slot that completes a subset restriction in a shared house.
What is Unique Rectangle Type 3?
This deduction assumes the puzzle has exactly one solution and that all earlier candidate removals were sound. First verify the complete two-value structure: four unsolved cells at the corners of two rows and two columns across exactly two boxes, each holding the same two base digits among its candidates. Exchanging those digits between the corners must move no given and must leave each affected house with one occurrence of each base digit. Type 3 then applies its additional rescue condition; an arbitrary rectangle is not enough.
In Type 3 the rescue alternatives act as one virtual slot. Combined with companion cells in a shared house they complete a subset restriction on a counted digit union, which is removed from the other eligible cells.
How to spot it
Verify four unsolved corners in two rows, two columns, and exactly two boxes. The rescue alternatives in the rescue cells form one virtual slot. Combine that slot with N−1 real companion cells in a shared house whose candidate union contains N digits. Count each cell once and remove the union only from other eligible cells.
The logic
Uniqueness guarantees that at least one rescue cell uses an extra digit, so the rescue group occupies one virtual slot. Together with the verified companion cells it reserves the stated digit union; only candidates outside that combined set are elimination targets.