Pick a digit and follow its strong links, the units where it has only two places, coloring the cells in alternating colors. Exactly one color holds the digit everywhere. A cell that sees both colors can't hold it (a trap). If two cells of the same color see each other, that color is false (a wrap), and the digit can be removed from all of it.
Simple Coloring turns a chain of either-or choices into two colors, so you can reason about the whole chain at once.
Skyscrapers, kites and Empty Rectangles are short chains of the same kind; coloring handles chains of any length.
A trap: a cell sees both colors
One color
The other color
Candidates removed
Solved as a result
Follow the 4's strong links (units where it has just two places) and color them in turn: R3C3 and R8C1 in one color, R2C1 and R3C7 in the other. One color holds the 4 everywhere, the other nowhere. R8C7 sees both colors, so whichever is true, it can't be the 4. That leaves R8C7 with only one candidate: 5.
Only the 4s are shown, so the pattern stands out.
A wrap: a color clashes with itself
One color
The other color
Candidates removed
Solved as a result
Follow the 3's strong links and color them in turn: R2C2, R9C3, R7C7 and R9C9 in one color, R3C3, R7C2 and R2C9 in the other. R9C3 and R9C9 are the same color and see each other, so they can't both be the 3. That color is false, and the 3 can be removed from all of it: R2C2, R9C3, R7C7 and R9C9. That leaves R2C2 with only one candidate: 5.
Only the 3s are shown, so the pattern stands out.
This position comes from a puzzle generated on this site, after every single has been filled in. Boxes are numbered 1–9 from the top left, row by row; R5C4 means row 5, column 4.
How to spot it
1Pick a digit. Mark every unit where it has exactly two places: those pairs are strong links.
2Start at one cell of a link and color it A, the other end B. Keep following links from each colored cell, alternating colors.
3Look for a cell outside the chain that sees an A and a B: remove the digit there.
4Look for two cells of the same color in one row, column or box: that color is false, so remove the digit from every cell of it.
Why it works
Along a strong link, exactly one end holds the digit. So along the chain, the colors alternate between true and false: all of A, or all of B.
A cell that sees both colors sees the true one, whichever it is.
Two same-colored cells in one unit cannot both hold the digit, so their color cannot be the true one.
Common mistakes
Linking through a unit where the digit has three places. Only two-place units count.
Continuing a chain with the same color across a link. Colors must alternate.
Mixing two separate chains: colors only mean something within one connected chain.
Questions
Why "simple"?
It uses one digit and only strong links. Multi-coloring and 3D Medusa extend it to several chains or several digits.
How long can the chain be?
Any length. The longer it is, the more cells it can affect.
Do I need actual colors?
No. Any two marks work, like dots and circles, or upper and lower case.
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