GridWits
Extreme tier Technique 45 of 46 Reference only

Forcing Chains

Follows the consequences of both options in a bivalue cell until they force the same outcome somewhere else on the board.

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. 1A1 has only two candidates, 3 and 7 — so the whole puzzle splits into exactly two possible worlds.
  2. 2Follow the first: if A1 is 3, E1 shares row 1 and loses its 3, so E1 must be 9 — and E5 sits in column E, so it can't be 9.
  3. 3Follow the other: if A1 is 7, A5 shares column A and loses its 7, so A5 must be 9 — and E5 sits in row 5, so again it can't be 9.
  4. 4Both worlds agree, so 9 leaves E5 whichever one is real. Three cells is the shortest a forcing chain gets; at this length it is the same deduction an XY-Wing makes, and longer chains are where it earns its name.

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 3 7 3 9 7 9 6 9 3 7 3 7 9
  • First colour in the chain
  • Second colour in the chain
  • Cells that establish the pattern
  • Where the conclusion lands
  • Candidate ruled out
Next in the ladder Nishio Forcing →

Suppose one candidate and propagate only forced singles; if the chain reaches an impossible cell or duplicate, that candidate is ruled out.