Unique Loop Type 3
This deduction assumes the puzzle has exactly one solution and that all earlier candidate removals were sound. This Type 3 Unique Loop deduction starts from a candidate arrangement whose two-value swap would preserve every affected row, column, and box. Extra candidates or a link restriction prevent that deadly swap and justify only the stated elimination.
What is Unique Loop 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 and every sector it touches. The swap must move no given and must leave each affected sector with one occurrence of each base digit. Type 3 then uses its additional candidate condition; an arbitrary rectangle or even cycle is not enough.
Type 3 uses the additional condition described below to prevent the verified two-value exchange. The conclusion may be inside the rescue cells or in their common peers; apply only the target rule for this type.
How to spot it
Verify an even loop in which each affected sector contains exactly two loop cells and the two base digits can be exchanged around the loop. The guardian alternatives in the rescue cells form one virtual slot. Combine that slot with N−1 real companion cells in a shared sector 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.