Proven Sudoku
Forcing Chain (general form)
Also called Forcing Chains, Implication chain.
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
Pick something and assume it. Follow what that forces, step by step. If every choice you could have made leads to the same result, that result is true no matter what.
The exact rule, for stronger players
The rule, stated exactly: Assume a candidate true or false and propagate the implications. If every possible assumption over a chosen set leads to a common conclusion, that conclusion holds. If a single assumption leads to a contradiction, that assumption is false.
What it removes: Apply the common conclusion, or eliminate the refuted assumption.
Why it works: Case analysis. Either the exhaustive branches agree, giving the shared conclusion, or one branch is self-contradictory, refuting it.
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
- Alternating Inference ChainA chain that switches between two kinds of step.
Related chains
- Grouped AICA chain where a step can use a whole group of squares at once instead of a single square.
- KrakenTake a pattern that nearly works.
- NishioAssume a number goes in a square, then check whether the rest of that number can still fit everywhere it needs to.
- Nishio Forcing NetThe same check as Nishio.
- Unit Forcing ChainTake one number in one row, column or box and try each home it could have.
How often does it come up?
Our rough estimate: forcing chains solve almost anything, which is exactly why they are ranked low in teaching order. A technique that always works teaches nothing about structure.