Contradiction forcing

A worked example

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

1. Where to look

   Inspect the complete consequence trace, not just the final contradiction.

   Temporarily assume a candidate is true. If explicitly justified consequences make a cell or house impossible, the assumption is false.

2. Read the evidence in this position

   Test the temporary assumption r7c8 = 9. This is not entered into the working board. Only the consequences in the trace are tested.

3. Why the deduction must follow

   Naked and hidden singles follow from that assumption until r9c8 has no candidates. That is impossible in a valid completion. So the original assumption is false. Expand the trace below to inspect every placement; the contradiction alone is not the explanation.

4. Apply the result

   Erase 9 from r7c8. The pattern may remove candidates without immediately solving a cell.