Alternating inference chain

A worked example

This position comes from SudokuByte’s lesson on the Alternating inference chain. Gold cells hold the evidence; green cells are the pattern’s ends.

1. Where to look

   Write each node as a particular digit in a particular cell. Alternate the link types.

   An AIC generalizes the strong-weak pattern to multiple digits and both cell and house links. This trainer demonstrates same-digit endpoint eliminations.

2. Read the evidence in this position

   Trace r3c42 → r3c43 → r3c53 → r3c52 → r9c52 → r9c42. 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 2. At least one endpoint is 2; a target seeing both endpoints cannot be 2.

4. Apply the result

   Erase 2 from r4c4, r6c4. The pattern may remove candidates without immediately solving a cell.