X-Chains: follow one digit between two useful ends

The links do different jobs

This lesson uses an X-Chain with strong links at both ends. Strong links pass false → true; weak links pass true → false. In our example, the strong links are conjugate positions in a unit.

HoDoKu — Chains: links and inferences · SudokuWiki — X-Cycles

Our six-node logic diagram

Let P,Q,R,S,T,U be six candidate-6 positions. P–Q, R–S and T–U are strong; Q–R and S–T are weak. Write P = Q − R = S − T = U. Here = labels a strong link, not equal cell values.

If P is false, Q is true, R false, S true, T false and U true. At least one of P/U must therefore contain 6. Another cell seeing both endpoints cannot contain 6. These letters describe a logic diagram, not coordinates from a full puzzle.

What if P is already true?

Then P directly blocks the target. There is no need to force U. The argument establishes that both ends cannot be false; it does not require them always to have opposite truth values.

Find a broken connection

If R–S were merely weak, a false R would not force a true S. The propagation would stop. Audit each implication rather than assuming a continuous drawn line is enough evidence.

In Classic 9×9, use Scan to scan the current entries, inspect justified eliminations and open this lesson. Chain and ALS searches are bounded; UR Type 1 and BUG+1 require verified uniqueness. Reading this lesson never changes your saved game.

Try before looking

References and further reading

Read the source explanations and compare them with our examples. Links are references, not endorsements or claims of affiliation.

• HoDoKu — Chains: links and inferences
• SudokuWiki — X-Cycles