(3 Strong Links) Grouped X-Loop
(3 Strong Links) Grouped X-Loop is the grouped variant of the X-Loop — a 3 Strong Links pattern where two of the three houses are blocks and at least one of the three strong links is grouped within a block. Instead of a digit confined to exactly two cells in a house, it's confined to two groups of cells inside a single block. The chain still forces at least one of the two roof endpoints to hold the digit, eliminating it from any cell that sees both.
What is a Grouped X-Loop?
A regular X-Loop needs three houses — two blocks and one row or column — where a candidate digit appears in exactly two cells per house, with the six cells chaining through bridge cells that share a line. The Grouped X-Loop relaxes the "two cells" requirement: at least one of the three strong links can be a grouped link, where the digit is confined to two groups of cells inside a single block instead of two individual cells. The chain still runs through the same X-shaped pattern, the bridge cells still see each other, and the same roof-elimination applies. The only structural difference is that one link's "two cells" are replaced by "two cell groups" within a block — for example, the digit can only sit in the top-left or bottom-right corner of a block.
How to spot it
Scan one digit at a time, looking for blocks where it's restricted to exactly two cells — the same starting point as a regular X-Loop. But also check each block for grouped links: if the digit is confined to two groups of cells within a block (not two single cells, but two clusters that can't both hold the digit), that counts as a grouped strong link. When you can chain three such links — two block-based houses and one row or column, with at least one grouped — through bridge cells that see each other, you've got a Grouped X-Loop. The elimination lands on any cell that shares a house with both roof endpoints. These patterns are rarer than the ungrouped X-Loop but appear in harder puzzles where a digit's candidates cluster inside blocks rather than lining up neatly.
The logic
The reasoning is identical to all 3 Strong Links variants — the grouped link behaves the same way as a single-cell link. Each strong link is a house where the digit has exactly two candidate positions (or two candidate groups, for the grouped link), 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 grouped link doesn't change the logic: a group of cells that can't all hold the digit acts exactly like a single cell that can't hold it.