Forcing Chains
Assume each candidate of a cell in turn and follow the forced consequences. If every assumption forces the same result somewhere, that result is certain.
The pivot cell has three candidates: 2, 5, and 8.
How to spot it
- 1Pick a cell and consider each candidate.
- 2Follow the forced placements each one triggers.
- 3If all branches agree on some digit, place it.
When to use
The last resort before guessing — pure logic on evil puzzles.
When not to
Not as a first tool; exhaust simpler techniques, since chains are slow to verify.
Common mistake
Stopping at the first branch instead of confirming all branches agree.
Worked Example
A forcing chain is the last resort before guessing, but it's still pure logic. Pick a cell and consider each of its candidates in turn, one at a time, following the forced consequences each one triggers elsewhere on the board — placements that must follow if that candidate were the answer.
If every single candidate you tried, followed all the way through its own chain of consequences, arrives at the same conclusion somewhere on the board — the same digit forced into the same cell — then that conclusion is certain, regardless of which candidate the pivot actually turns out to be. It's slow to verify by hand, which is why it's reserved for evil puzzles once everything simpler has been exhausted.