Unique Rectangle Type 1

This deduction assumes the puzzle has exactly one solution and that all earlier candidate removals were sound. A Type 1 Unique Rectangle starts from a candidate state in which swapping two digits across the construction would preserve every touched row, column and box. One rescue cell carries extra candidates; it must take one of them, so the two base digits are removed from that cell.

What is Unique Rectangle Type 1?

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 1 then applies its additional rescue condition; an arbitrary rectangle is not enough.

In Type 1 every loop cell except one is bivalue on the base digits; the remaining rescue cell holds extra candidates as well. Because at least one rescue candidate must be true, that cell cannot hold either base digit.

How to spot it

Find four unsolved cells at the corners of two rows and two columns, arranged across exactly two boxes. Three corners contain only the same two base digits; the fourth contains those digits plus one or more extras. Verify that swapping the base digits would preserve both rows, both columns, and both boxes before applying the Type 1 deduction.

The logic

If the rescue cell used a base digit, the complete base-digit arrangement would permit the forbidden swap. Under the unique-solution assumption it must use an extra candidate, so the two base candidates can be removed from that cell.