Simple Coloring

Also called Single's Chain, Colouring, Chain Colouring, Color Trap and Wrap.

New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.

What it means

Pick a digit. Colour its homes in two colours that swap, like black and white squares. One colour is right and one is wrong. If a square sees both colours, it cannot hold the digit. If two squares of one colour clash, that whole colour is wrong.

The exact rule, for stronger players

The rule, stated exactly: For digit d, build the graph whose vertices are candidate cells and whose edges are conjugate pairs. Two-color each connected component. Rule 1 (color trap): any cell outside the component seeing both colors cannot hold d. Rule 2 (color wrap): if two cells of the same color share a house, that color is entirely false and the opposite color is true.

What it removes: Rule 1 removes d from cells seeing both colors. Rule 2 removes d from every cell of the contradictory color and places d in the other color's cells.

Why it works: Within a component, colors alternate along conjugate links, so exactly one color is the true set. A cell seeing both colors sees a true cell either way. If one color contains two cells in a house, that color cannot be the true set, since a digit appears once per house.

Worked examples

These come from real Proven Sudoku boards. Nobody drew them by hand to make the pattern look neat. Each one is checked first, so the board is one you could really meet, the pattern is really there, and every digit it rules out is really wrong.

Sudoku grid showing Simple Coloring. The 2 links alternate through 5 cells in two colours, and one colour must be true. Any cell seeing both colours cannot be 2. — The 2 links alternate through 5 cells in two colours, and one colour must be true. Any cell seeing both colours cannot be 2.

Sudoku grid showing Simple Coloring. The 6 links alternate through 4 cells in two colours, and one colour must be true. Any cell seeing both colours cannot be 6. — The 6 links alternate through 4 cells in two colours, and one colour must be true. Any cell seeing both colours cannot be 6.

Learn these first

X-WingA digit is stuck in the same two columns in two different rows, making a rectangle.
Turbot FishPick one digit.

Related single-digit patterns

SkyscraperPick a digit.
X-ColoringColouring with an extra step.
2-String KitePick a digit.
3D MedusaColouring spread across every digit at once, not just one.
Empty RectangleIn one box, all the homes for a digit sit in one row and one column.

How often does it come up?

Our rough estimate: common, and it subsumes several separately named patterns, which makes it high value to learn.

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