Solving techniques
Simple coloring
Simple coloring turns a hard chain into a picture. You paint the chain in two colors and let the colors tell you what to remove.
Simple coloring links cells where a digit has exactly two candidates in a unit (strong links) and paints them alternately in two colors. One color is true and the other false. Any cell that sees both colors cannot hold the digit.
The logic
When a digit has only two possible cells in a unit, exactly one is true and the other is false. Follow such links from cell to cell, alternating two colors. All cells of one color are true, or all of the other color are. You do not know which. A cell outside the chain that sees one cell of each color will always see a true cell, so the digit cannot be there.
How to use simple coloring
- Choose a digit and mark every unit where it has exactly two candidates.
- Start from one such pair. Color one cell A and the other B.
- Follow each cell to the next link, alternating colors.
- Look for a cell outside the chain that sees both an A and a B cell. Remove the digit.
Common mistakes
- Linking cells in units where the digit has three or more candidates. Only exact pairs make a strong link.
- Mixing two separate chains and treating them as one.
- Removing the digit from the colored cells themselves.
Related
Learn XY-Wing first, and see hidden singles for the idea of a digit with limited places. Coloring is the top of the ladder in our technique list.
Frequently asked questions
What is simple coloring in Sudoku?
A technique where cells linked by pairs for a digit are painted in two colors to find which cells cannot hold it.
What is a strong link?
Two cells that are the only candidates for a digit in a unit. If one is false, the other is true.
Is it hard?
It takes practice, but the colors make it much easier than reasoning in your head.