Simple coloring in sudoku
Simple coloring takes the strong link, a unit where one digit has exactly two homes, and chains as many of them as the board offers. Paint the linked cells in two alternating colors and a powerful fact appears: all cells of one color are true together and false together. One digit, two futures, and eliminations wherever the futures overlap.
Building the chain
Follow the 5s below. The left marked column holds its 5 in exactly two cells, so does the marked row along the bottom, and so does the right marked column. The three links share ends, which chains them: column, row, column. Alternate colors along the chain, shown here as the darker and lighter tints:
Each link forces its two ends apart: one end true, the other false. Chaining the links extends that seesaw, so the darker cells stand or fall as a group, and the lighter cells are their exact opposite. One of the two groups is the truth about this digit. You do not yet know which, and the technique never asks you to find out.
The eliminations
Rule one: a cell outside the chain that sees both colors is finished. Whichever color turns out true, one of the cells it watches becomes a 5. The struck cell below sits in the same box as a darker cell and the same row as a lighter one, so both futures reach it:
Rule two pays even better when it fires: two cells of the same color inside one unit. They would have to both be true, a unit cannot hold the digit twice, so that entire color is false, and every cell of the opposite color takes the digit at once. One observation, several placements.
Working the technique
Coloring runs on one digit at a time, which keeps it mechanical. Pick a digit, select it so every candidate lights up, and find its strong links by counting homes per unit, the exact skill skyscrapers run on. Chain the links that share ends, alternate your two marks, then check the two rules: outside cells seeing both colors, and same-color collisions inside a unit.
The discipline that matters is refusing weak links. Three or more homes in a unit force nothing, and a chain built through one produces confident nonsense. Count to exactly two before every link, with Auto notes keeping the counts honest.
Where it fits
Coloring closes out the expert rung alongside the XY-wing, the swordfish and the skyscraper. It is also the doorway technique: a colored chain is a forcing chain restricted to one digit and strong links only, so every habit built here transfers to the master tier whole.
Frequently asked questions
What is simple coloring in sudoku?
A technique for one digit at a time. Follow its strong links, units where the digit has exactly two homes, and paint the linked cells in two alternating colors. Every cell of one color is true together and false together, and that all-or-nothing property earns the eliminations.
What are the two coloring rules?
First: a cell outside the chain that sees both colors can never hold the digit, because one of the two colors must be entirely true. Second: if two cells of the same color share a unit, that whole color is false, and every cell of the opposite color takes the digit at once.
Do I need an app that supports colors?
No. The colors are bookkeeping for a mental chain, and plenty of solvers track them as two symbols in their notes. On this site, selecting the digit highlights all of its candidates, which is the visibility the technique needs.
How is simple coloring different from a forcing chain?
Scope. Coloring follows one digit through strong links only, which keeps it mechanical and safe. Forcing chains follow consequences across digits and cell types, which reaches further and demands more care. Coloring is the disciplined warm-up for that jump.