Simple Coloring in Sudoku: Strong-Link Chains
Simple Coloring follows strong links for one candidate digit. Whenever a row, column, or box has exactly two positions for that digit, one position must be true and the other false. Alternate two colors along connected strong links. You can then use a color contradiction or a color trap to remove candidates.
Coloring does not guess which color is true; it proves what follows under either alternating state.
What is Simple Coloring?
Choose one digit and build a chain of conjugate pairs. Give the two ends of the first strong link opposite colors, then alternate colors through every connected strong link. Same-colored candidates represent the same truth state within that chain. The colors are labels only and do not mean correct or incorrect until a rule exposes a contradiction.
Two Simple Coloring rules
- Build one-digit strong links. Connect houses where the chosen digit appears in exactly two cells.
- Alternate two colors. Every strong-link pair receives opposite colors throughout the connected chain.
- Apply the wrap rule. If two candidates of one color see each other, that color is false everywhere in the chain.
- Apply the trap rule. An uncolored candidate that sees both colors can be removed because one color must be true.
Example: a color trap on candidate 3
A chain of conjugate 3s alternates green and blue. An uncolored candidate 3 sees one green cell in its row and one blue cell in its box.
- Check the chain. Every color change must cross a house containing exactly two candidates for 3.
- Check both lines of sight. The target sees at least one candidate of each color in the same chain.
- Remove the target. Whether green or blue is true, the uncolored candidate conflicts with a true 3.
Common coloring mistakes
Coloring weak links
Alternation is guaranteed only across a strong link with exactly two candidates in a house.
Mixing separate chains
Colors in disconnected chains do not share a truth state.
Assuming one color is true early
Wait for a wrap, trap, or another valid chain rule to justify an elimination.
Simple Coloring practice checklist
- Choose a digit with several conjugate pairs.
- Keep each disconnected chain separate.
- Search first for same-color conflicts, then for cells that see both colors.
Coloring is bookkeeping for a chain of either-or relationships. Keep the chain on one digit, alternate only across strong links, and make eliminations only when a named rule closes the argument.
Simple Coloring FAQ
What is a strong link?
For one digit, a strong link connects the only two candidate positions in a row, column, or box; at least one must be true.
Do the colors have fixed meanings?
No. They simply label opposite truth states in one connected chain.
Can I combine disconnected color chains?
Not without an additional logical link. Each disconnected chain has independent color states.
