Proven Sudoku
Nishio
Also called Nishio test, Single digit contradiction test.
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
Assume a number goes in a square, then check whether the rest of that number can still fit everywhere it needs to. If it cannot, your assumption was wrong.
The exact rule, for stronger players
The rule, stated exactly: Assume a candidate of digit d is true and propagate only the consequences for d. If some house is left with no place for d, the assumption is false.
What it removes: Eliminate the assumed candidate.
Why it works: Reductio restricted to one digit, which makes it cheap to run by hand.
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
- 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.
- X-ChainA chain about one number only.
- XY-ChainA chain of squares that each hold exactly two numbers.
- AIC with AHS NodesThe same as above but using sets of numbers that are hiding rather than sets of squares.
How often does it come up?
Our rough estimate: historically popular because it is tractable on paper. Largely superseded by chain logic.