GridWits

Nishio Forcing Chains

Extreme Reference only

Proof by contradiction on a single candidate: tentatively assume it's true, chain the consequences forward, and if that breaks the board, it was false all along.

The solver does not attempt this technique, so Smart Hint will never suggest it. It is documented because you may still want to spot it yourself.

A 1 B 2 C 3 D 4 E 5 F 6 G 7 H 8 I 9 4 7 2 4 2 4

How it works

  1. Tentatively assume A1 = 4. Chase the consequences: that forces E1 = 2, which forces E5 = 4 — but E5 already shares a box with A1's assumed 4 by way of another link, a contradiction.
  2. Since assuming A1 = 4 breaks the board, A1 can't be 4 — eliminate it, leaving only 7. This is exactly how GridWits' own Skyscrapers solver's `contradiction` technique works, applied here to Sudoku.

Play a Sudoku that needs this technique →