GridWits
Extreme tier Technique 34 of 46 Reference only

Nishio Forcing Chains

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.

How it works

  1. 1Tentatively assume A1 = 4 and chase only what that forces.
  2. 2E1 shares row 1, so it drops to 2; E5 shares column E with E1, so it has to be the 4; D4 shares the middle box with E5, so it drops to 9.
  3. 3But A1 = 4 also empties the 4 out of A4 down column A, leaving A4 = 9 — and A4 and D4 both sit in row 4.
  4. 4Two 9s in one row is impossible, so A1 was never 4. Strike it and leave the 7. This is exactly how the solver's `contradiction` rung works, applied by hand.

Play a Sudoku that needs this technique →

A 1 B 2 C 3 D 4 E 5 F 6 G 7 H 8 I 9 4 7 2 4 4 9 4 9 2 4 4
  • First colour in the chain
  • Second colour in the chain
  • Where the conclusion lands
  • Candidate ruled out
Next in the ladder Forcing Chain Variants (Digit, Cell, Unit, Quad) →

Named by what's exhaustively tested — every candidate of one digit, every candidate of one cell, every cell of one unit, or every cell across four related units — each variant follows every branch to see if they all agree on some outcome.