(3 Strong Links) X-Loop
(3 Strong Links) X-Loop is a specific shape of the 3 Strong Links family where the three conjugate pairs form an X pattern — two of the three houses are blocks, and the bridge cells sit on a shared row or column that crosses the two blocks. The chain forces at least one of the two roof endpoints to hold the digit, eliminating it from any cell that sees both.
What is an X-Loop?
An X-Loop is a 3 Strong Links pattern where two of the three houses are blocks. The third house is a row or column. Each house confines a candidate digit to exactly two cells, and the six cells chain together through bridge cells that share a line. The "X" in the name comes from the crossing shape formed by the two block-based links and the row or column that connects them. Like all 3 Strong Links variants, the chain forces at least one of two roof cells to contain the digit, so any cell seeing both roof cells can't hold it. The X-Loop is the block-based sibling of 3 Skyscrapers (three rows) and 3-String Kite (alternating rows and columns).
How to spot it
Scan one digit at a time, looking for blocks where it's restricted to exactly two cells — that's the signature of an X-Loop. When you find two such blocks, check whether one cell from each block shares a row or column; if so, those are bridge cells. Then look for a third house (a row or column) where the same digit is also confined to two cells, with one cell visible from each block's other candidate. If the chain closes — three conjugate pairs linked through two bridge cells that see each other — you've got an X-Loop. The elimination lands on any cell that shares a house with both roof endpoints. X-Loops are rarer than 3 Skyscrapers or 3-String Kite but appear in harder puzzles where a digit's candidates cluster inside blocks.
The logic
The reasoning is identical to all 3 Strong Links variants. Each strong link is a house where the digit has exactly two candidate positions, so one of them must be the digit. In the chain, one candidate from each neighbouring pair sits on a shared line — the bridge. Because the two bridge cells see each other, at most one can be the digit. If the first bridge is the digit, the second link's digit falls on its roof cell and the chain stops. If not, the first link's digit falls on its other cell, which is the next bridge — and the same reasoning carries forward. Every case forces at least one of the two roof cells to contain the digit, so any cell seeing both roof cells can't also hold it. The block-based links don't change the logic — a block where a digit has exactly two candidates is just as strong a link as a row or column with two candidates.