XY-Chain

A worked example

This position comes from SudokuByte’s lesson on the XY-Chain. Gold cells hold the evidence; green cells are the pattern’s ends.

1. Where to look

   Enter a bivalue cell on one digit and leave on the other.

   Move through bivalue cells using their internal strong links and shared-digit weak links. Matching endpoint digits give eliminations.

2. Read the evidence in this position

   Trace r8c59 → r8c56 → r8c66 → r8c64 → r8c24 → r8c25 → r9c25 → r9c24 → r9c74 → r9c79. Solid links mean at least one end is true; dashed links mean the two ends cannot both be true.

3. Why the deduction must follow

   Assume the first candidate is false. The next is forced true, the next false, and so on, ending true. If the first candidate was true instead, it already supplies the required 9. At least one endpoint is 9; a target seeing both endpoints cannot be 9.

4. Apply the result

   Erase 9 from r8c7, r8c9, r9c5, r9c4. The pattern may remove candidates without immediately solving a cell.