Academy
NishioNishio sudoku technique
Nishio asks one sharp question: if this candidate were the answer, could the rest of this digit still be placed legally? Put the digit in mentally and propagate only that digit's placements across the grid. When the trial walls itself in — some row or box left with no legal spot — the assumption was false, and the candidate is eliminated for good.
How to find a nishio
- Choose a promising candidate, typically of a digit that is nearly complete on the grid.
- Assume it and mark, box by box, where that digit is now forced to go.
- Watch for a unit that can no longer take the digit anywhere.
- A contradiction erases the tested candidate; no contradiction simply means no verdict — undo and try elsewhere.
The pattern on the grid
A real position — every pencil mark computed, every red candidate a verified elimination. Toggle to see the grid after the move.
Nishio on 1: r2c7=1 → r6c9=1 → no place for 1 in r9 => r2c7<>1
534719286896000000127068400482197653315826040769003020200670000600980000908004060
Standard 81-character format (0 = empty) — paste it into your solver of choice and verify the move yourself.
Worked example
Test the candidate 1 at r2c7: propagating only that digit forces the blue placements in the diagram, after which one unit is left with no legal cell for 1 at all. The trial contradicts itself, so r2c7<>1. Note what the failure does not say — it does not place anything; it only removes the tested candidate.
When it fails
No contradiction proves nothing — it does NOT confirm the candidate, it only ends that trial. And propagate strictly the tested digit; the moment you chase other digits' consequences you've drifted into full trial-and-error.