Sudoku techniques · Extreme
Forcing Chain in Sudoku
A Forcing Chain is the technique of last resort, and the one the app falls back to when nothing with a fixed shape applies. Pick a cell with two candidates, or a number with two possible positions in a unit, assume one, and follow the chain of forced moves. If it reaches a contradiction, the other option is proved.
Also known as: Contradiction Chain, Nishio.
Why it works
When a cell has only two candidates, or a number has only two possible positions in a row, column, or box, testing one possibility and following the chain of forced moves to a contradiction proves the other.
How to spot it
There is no pattern to see here, which is exactly the point.
- Start from a bivalue cell, or a digit with only two homes in a unit: a wrong guess is cheap to undo there.
- Follow only forced consequences. The moment you have to guess a second time, back out; the chain has gone too deep to be useful.
- A contradiction proves the other branch. Reaching the end without one proves nothing, so pick your starting cell where the consequences fan out fastest.
Builds on
Worked example
These are the app's own lesson boards. Step through them the same way a hint does.
This one has no fixed shape to draw. The app falls back to it only when every pattern above has been ruled out.