Forcing Chain
A Sudoku solving technique · level 8 · first needed around SE grade 8.5+
By The Hardest Sudoku Team · Last updated
TL;DR
A Forcing Chain follows a sequence of 'if this, then that' implications until two starting assumptions converge on the same conclusion, which must therefore be true.
How does the Forcing Chain work?
You pick a cell with two candidates and trace the consequences of each. If both possibilities force the same value into some other cell — or both force a contradiction in one of them — you can place (or eliminate) with certainty, without guessing.
When does it apply?
When no simpler technique advances the puzzle — the standard tool for monster-grade (SE grade 8.5 and above) puzzles.
A worked example
If assuming a cell is 3 eventually forces cell K to 7, and assuming it is 8 also forces cell K to 7, then K is 7 no matter which assumption holds.
See where this fits on the difficulty scale on the SE grade page, or browse every technique in the glossary.