Unique Loop Type 1
A Unique Loop Type 1 is the loop-based counterpart of Unique Rectangle Type 1. Six or more cells form a closed loop where every cell carries the same two candidates, creating a deadly pattern with two interchangeable solutions. When one cell in the loop has extra candidates beyond the deadly pair, that rescue cell cannot hold either deadly-pair digit — so both are removed from it.
What is Unique Loop Type 1?
A valid Sudoku has exactly one solution. That guarantee is a constraint in its own right: any arrangement of candidates that would allow two interchangeable solutions cannot be part of the answer. The most common shape that threatens uniqueness is the Unique Rectangle — four cells at the corners of a rectangle, each containing the same two candidates. A Unique Loop generalises that shape to a longer chain: six or more cells that alternate between two houses at each step and close back on themselves, with every cell carrying the same two candidates.
Type 1 is the simplest case. All but one of the loop cells hold only the deadly pair, while a single cell — the rescue cell — has one or more extra candidates beyond the pair. Because the deadly pattern cannot be part of the solution, the rescue cell cannot contain either of the deadly-pair digits. If it did, the loop would collapse into the deadly pattern. So both deadly-pair candidates are removed from the rescue cell, often leaving it as a naked single.
How to spot it
Start by scanning for chains of bivalue cells — cells with exactly two candidates — that share the same pair. Trace the chain as it alternates between rows, columns, and blocks; if it closes back on itself after six or more steps, you have a Unique Loop. Then check whether exactly one cell in the loop carries extra candidates. If so, it is a Type 1: delete the deadly pair from that rescue cell. Loops with two or more rescue cells lead to Types 2, 3, or 4 instead. Unique Loops are rarer than Unique Rectangles because the chain has to close, but they turn up in harder puzzles once the easier techniques have been exhausted.
The logic
If the rescue cell held either digit of the deadly pair, the remaining loop cells would be forced to fill in the pair in the only way that satisfies their shared houses — and that fill-in is the deadly pattern, which has two interchangeable forms. A puzzle with a unique solution cannot contain a deadly pattern, so the rescue cell must avoid both digits of the pair. Removing them from the rescue cell is the only safe play, and it follows directly from the uniqueness guarantee without needing to know which configuration is correct. The argument is identical to Unique Rectangle Type 1; only the shape of the loop is longer.