Grouped Three-Node X-Chain
A Grouped Three-Node X-Chain — traditionally listed as Grouped 3 Strong Links — is the general grouped form of (A=B)-(C=D)-(E=F). At least one logical side represents several same-digit candidates. The three strong inferences and two weak inferences prove the inclusive endpoint relation A OR F.
What is a Grouped Three-Node X-Chain?
A grouped side is a disjunction: it is true when at least one represented candidate is true and false only when all represented candidates are false. Each equals sign is a strong link (XOR) joining two exhaustive logical sides. Each dash is a weak inference (NAND) and requires universal incompatibility between the candidates represented on its connected sides.
How to spot it
For one digit, identify three justified strong-inference nodes, allowing row-box or column-box groups, and verify weak inferences B-C and D-E member by member. The outer logical sides A and F are the endpoints. A target is valid only when it conflicts with every candidate represented by both sides.
The logic
Starting with outer side A false propagates true and false states through (A=B)-(C=D)-(E=F) until F is true. Therefore A OR F holds, possibly with both sides true. A red candidate can be removed only if it conflicts with every member of both endpoint sides. This is the Type 1 same-digit elimination.