Simple Coloring Sudoku Technique

Updated 11 August 2026

Simple coloring assigns two alternating colors to a chain of strong links on one digit, then erases any candidate for that digit that can see cells of both colors at once.

When simple coloring applies

Simple coloring builds the same kind of network an X-Chain does, but uses only strong links — no weak links — and tracks the whole connected network at once instead of a single path between two endpoints. Starting from any cell in the network, alternate two colors along every strong link: if a cell is one color, the cell it is strongly linked to must be the other, because a strong link means one of the two must hold the digit whenever the other does not.

Once every reachable cell in the network is colored, two elimination rules apply. A cell outside the network that sees two cells of the same color proves that color is impossible everywhere — a color wrap — clearing every cell of that color at once. A cell outside the network that sees one cell of each color cannot hold the digit either, because whichever color turns out to be correct, that cell sees a cell holding the digit — a color trap, and the more common case in practice.

Because coloring only follows strong links, it misses patterns that need a weak link somewhere in the middle, which is exactly what X-Chains and the more general AIC add on top of it.

Worked example

r4c5 and r9c5 are the only candidates for 1 in column 5, a strong link. r4c5 and r4c7 are the only candidates for 1 in row 4, another strong link. r4c7 and r6c7 are the only candidates for 1 in their shared box, a third strong link. r6c6 and r6c7 are the only candidates for 1 in row 6, a fourth strong link. Coloring from r4c5 outward: r4c5 is color A, which makes r9c5 color B through column 5 and r4c7 color B through row 4. r4c7 being B makes r6c7 color A through the box link, and r6c7 being A makes r6c6 color B through row 6.

r9c7 was carrying 1, 3 and 5 before the deduction. It sees r6c7, color A, through column 7, and it sees r9c5, color B, through row 9. Whichever color turns out to hold the actual 1, r9c7 sees a cell of that color, so it cannot hold 1 itself. The solver removes it and leaves 3 and 5 behind.

How to spot simple coloring

1. Pick a digit and map its strong linksFor one digit, find every unit where it has exactly two candidate cells, and note both cells of each such strong link.
2. Color the connected networkStarting from any cell, alternate two colors across every strong link that connects to it, following the network as far as it reaches.
3. Look for a color wrapCheck whether any cell outside the network sees two cells of the same color. If so, every cell of that color can be cleared.
4. Look for a color trapCheck whether any cell outside the network sees one cell of each color. If so, that cell can have the digit erased.

Common mistakes

• Coloring across a weak link. Simple coloring only follows strong links; a unit with three or more candidate cells for the digit does not extend the network.
• Eliminating the digit from a cell inside the colored network. The network’s own cells are exactly where the digit is still being decided.
• Mixing up the wrap and trap rules. A wrap clears an entire color because two same-colored cells contradict each other; a trap clears one outside cell because it sees both colors.
• Stopping at the first strong link found. The network can spread through many cells before a trap or wrap becomes visible.