Nishio sudoku technique

Expert level Appears in puzzles rated SE 4.0 – 5.0

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

  1. Choose a promising candidate, typically of a digit that is nearly complete on the grid.
  2. Assume it and mark, box by box, where that digit is now forced to go.
  3. Watch for a unit that can no longer take the digit anywhere.
  4. A contradiction erases the tested candidate; no contradiction simply means no verdict — undo and try elsewhere.
From the table: Keeping the trial to a single digit is what separates Nishio from blind guessing: the consequences stay small enough to hold in your head and to unwind cleanly. It shines on diabolical grids where pattern techniques have run dry.

The pattern on the grid

88888

Assuming 8 at r2c2 (red) forces the blue 8s — and leaves the bottom-left box with no home for 8. The assumption dies.

Worked example

Digit 8 has six placements already; test the candidate at r2c2. Propagate only the 8s: the trial forces 8 into r4c5 (last spot in its box) and then r7c8 — after which the bottom-left box has no legal cell for an 8 at all. Contradiction. The tested candidate was false, so the 8 at r2c2 is erased and everything you imagined is rolled back.

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.

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