Unique Loop Type 1

This deduction assumes the puzzle has exactly one solution and that all earlier candidate removals were sound. A Type 1 Unique Loop 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 Loop 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: an even loop of unsolved cells sharing the same two base digits, with exactly two loop cells in every house it touches. Exchanging those digits around the loop 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 even cycle 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

Verify an even loop in which each affected house contains exactly two loop cells and the two base digits can be exchanged around the loop. All but one loop cell are bivalue on the base digits; the rescue cell also has extra candidates. Confirm the swap would preserve every touched house before removing the two base digits from that rescue cell.

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.