Simple Colouring in Sudoku
Simple Colouring, also called single’s chains, is the gateway to chain techniques. You pick one digit, colour its “either/or” pairs in two alternating colours, and let the colouring reveal a contradiction or a cell that two colours both attack.
How to use Simple Colouring, step by step
- Pick a digit and find its conjugate pairs — units where it has exactly two candidate cells.
- Colour the two cells of a pair in alternating colours, then extend the chain through linked pairs.
- One colour is the truth and the other is false, though you do not yet know which.
- If two cells of the same colour share a unit, that colour is impossible — so the other colour is true.
- Or, if an uncoloured cell sees both colours for that digit, the digit can be removed from it.
What is Simple Colouring?
Simple Colouring tracks a single digit through its conjugate pairs, painting them in two colours so that one colour must be true and the other false. The two colours expose two kinds of elimination: a colour that repeats in a unit collapses, and any cell seeing both colours cannot hold the digit. It is the easiest of the chain techniques and a stepping stone to longer chains.
How to spot a colouring chain
Start where a digit has lots of conjugate pairs (units with exactly two spots for it), and follow the on/off links from cell to cell. Keep the two colours strictly alternating. It rewards tidy pencil marks and a single-digit focus. For where it fits among the other moves, see tips & strategy and the single-digit X-Wing.
Simple Colouring in Sudoku: FAQ
What is Simple Colouring in Sudoku?
Simple Colouring, or single’s chains, is a technique where you colour a single digit’s conjugate pairs in two alternating colours. Because one colour must be true, you can eliminate the digit from any cell that sees both colours, or rule out a colour that repeats within a unit.
What is a conjugate pair?
A conjugate pair is a unit — row, column or box — where a particular digit has exactly two candidate cells. One of the two must hold the digit, which is what makes the on/off colouring work.
Is Simple Colouring an advanced technique?
It is the first of the chain techniques, sitting above wings and fish in difficulty. It is only needed on the hardest grids, but it introduces the colouring idea that powers more advanced chains.