Grouped Chains
Grouped Chains extend the Alternating Inference Chain by letting a whole group of candidates act as a single link in the chain. Where a plain AIC hops from one cell to another, a grouped chain can hop to a cluster of candidates that share a box-and-line — and that reach closes chains a cell-by-cell version cannot.
The idea
Inside a box, if a digit's candidates all lie in one row or column segment, they behave as a group node. A strong link runs to the group when the digit must be somewhere in it; a weak link runs from the group when the digit being there forbids it elsewhere in the shared line. Splice such group nodes into an AIC and the same alternating logic applies: begin and end on strong links, and at least one endpoint is true. The eliminations are exactly those of any AIC — clear the shared digit from cells seeing both same-digit ends, or resolve the shared cell where the endpoints meet.
A worked example
Chase the digit 5. Start at 5r1c1 and strong-link down column 1 (its only 5s are r1c1 and r4c1) into box 4, whose only 5s — r4c1 and r4c2 — form a group node. From the group a weak link runs along row 4 to 5r4c8, which strong-links up column 8 to 5r1c8. The chain begins and ends on a strong link, so at least one of the endpoints 5r1c1 and 5r1c8 is true. Both are 5s in row 1, so r1c4, seeing both, loses its 5. The group node carried the chain through box 4 where a cell-by-cell version stalled.
A grouped chain on 5. Box 4's only 5s — r4c1 and r4c2 (amber) — act as one group node: a strong link (solid) enters it down column 1, a weak link (dashed) leaves along row 4. Both endpoints are 5s in row 1, so r1c4 loses its 5.
Step by step
- Start an AIC alternating strong and weak links.
- Use group nodes where a digit's candidates in a box share one row or column.
- Keep the alternation through cells and groups alike.
- Apply the endpoint rule for the elimination or placement.
Common mistakes
- Groups across two lines. A group must lie within a single row or column of its box, or it cannot act as one node.
- Broken alternation. As always, links must alternate strong and weak; a group node does not excuse two weak links in a row.
- Wrong elimination target. Read the endpoints the same as any AIC — the group is a link, not the conclusion.
Which Sudoku types is this best for?
The same logic applies across variants, but it pays off more in some than others.