Proven Sudoku
Cell Forcing Chain
Also called Cell Forcing Chains.
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
Take one square and try each number it could hold. Follow each one out. Anything that comes true in every case is true.
The exact rule, for stronger players
The rule, stated exactly: Take every candidate of one cell as a starting assumption. If all of them force the same conclusion, that conclusion holds.
What it removes: Apply the conclusion common to every branch.
Why it works: The cell must take one of its candidates, so the branches are exhaustive.
Worked examples
None yet. This pattern does not turn up in our daily boards, so there is no real example to show. We would rather wait than draw a fake one.
Learn these first
- Forcing Chain (general form)Pick something and assume it.
Related chains
- Continuous Nice LoopA loop where the reasoning closes back on itself with no weak spot.
- Digit Forcing ChainTake one number in one square.
- Discontinuous Nice LoopA loop that almost closes but has one weak spot.
- Dynamic Forcing Chain with ContradictionAssume a digit is right.
- Dynamic Forcing Chain with Double ImplicationTry both options for a square and follow each one out fully.
How often does it come up?
Our rough estimate: common in solver output on hard grids, less common in hand solving.