Nishio is a careful “what if?” You try a candidate as true and follow forced consequences (not wild guesses). If that world breaks the rules, the trial candidate was false.
This is proof by contradiction — still logic, not random guessing.
Why it works
Sudoku never allows a contradiction. If assuming digit D in a cell forces two of the same digit in a house, or empties a cell of all candidates, then D cannot be there.
You only accept forced moves in the trial. Coach separates forcing-chain validation (proving a pattern) from wild guessing — Nishio is the careful version.
How to spot it
Only follow forced moves in the trial world — never wild guesses. If the world breaks, the trial candidate is false.
Demonstration
When simpler patterns stall, pick a promising candidate and ask: what if this were true?
Follow only forced placements and eliminations. Here trying the pattern on 1 leads to a contradiction — Nishio.
A legal Sudoku cannot reach that broken world. So the trial candidate cannot be true.
Eliminate the impossible candidate(s) (red) (here 1).
Example 1
Trial a candidate and follow the forcing chain (forced moves only).
Nishio shows 6 cannot be true here — it explodes into a contradiction.
Remove the contradicted candidate(s) (red) (here 6). That trial world was illegal.
Example 2
Trial a candidate and follow the forcing chain (forced moves only).
Nishio shows 7 cannot be true here — it explodes into a contradiction.
Remove the contradicted candidate(s) (red) (here 7). That trial world was illegal.