Colouring
Simple colouring
Simple colouring follows one digit around the grid and paints it in two colours. Whenever a unit has only two homes for the digit, those two cells are linked: exactly one of them holds it. Colour one of them blue, the other green, and carry on. Any cell that can see both colours can't hold the digit, and any colour that ends up twice in one unit is the wrong colour.
- Level
- Advanced
The pattern
What it does.
The colours aren't a guess. They are a record of the fact that in every linked pair, one cell is the digit and the other isn't, so the whole chain alternates between the two possibilities.
Two rules follow. If a cell can see a blue and a green cell of the same digit, it can't be that digit, because one of the two colours must be the digit itself. And if one colour appears twice in a single unit, that colour is impossible, so every cell of the other colour is the digit.
It's the first technique on this site that reads the whole grid at once for one digit, and it's the doorway to the chain techniques beyond it.
Example
A worked example.
Pick a digit and find its strong links
Choose a digit, and look for every unit in which it has exactly two possible cells. Each of those is a strong link: one of the two cells holds the digit.
Colour the first chain
Start at any uncoloured link. Colour one cell blue and the other green, then follow the digit on from each of them: every new link alternates the colours.
Look for a cell that sees both colours
Any uncoloured cell that shares a unit with a blue cell and a green cell of this digit can't hold it. Remove it. This is the commonest result of the technique.
Look for a colour that traps itself
If one colour appears twice in a single row, column or box, that colour is impossible: only one cell there can hold the digit. Then every cell of the other colour is the digit, and can be placed.
Spotting it
How to spot it.
- Work one digit at a time. Colouring mixes badly across digits, and a single-digit view is what makes the chains readable.
- Units with exactly two homes for the digit are the links. Count them before you start: a digit with none has nothing to colour.
- Draw the colours rather than holding them in your head. Two shades of pencil, or the app's own highlighting, is the difference between seeing the contradiction and not.
- Check both rules every time you extend a chain. The second rule, a colour twice in a unit, is the one that places digits rather than removing them.
Where it stops working
Colouring proves things about one digit at a time and proves nothing when both colours remain consistent, which is common. It also depends on the strong links being real: a unit with three homes for the digit breaks the chain and the colouring has to stop there. Like every technique from here on, it's worth nothing without a complete candidate list.
Keep going
Related topics.
New to sudoku? The rules take two minutes to read, and the first-puzzle walkthrough covers the basics that come before any of these.
Beyond the lessons.
The game's lessons stop at X-Wing, so there's no Simple colouring lesson. The eight it does teach will get you through almost any puzzle; this page is here for when you run into the pattern anyway.