Simple Coloring
advancedUsing two colors to track conjugate pairs and find contradictions or eliminations
Simple Coloring (also called Singles Chains) assigns two colors to a single candidate's conjugate pairs throughout the grid. By following the chain, you can find contradictions that lead to eliminations.
Understanding the Concept
Pick a candidate digit. Find houses where it appears exactly twice — these are "conjugate pairs." If one is true, the other must be false.
Assign Color A to one cell in a pair and Color B to the other. Then follow: wherever a Color A cell forms a conjugate pair with another cell, that cell gets Color B, and vice versa.
Continue until no more extensions are possible. You now have a chain of alternating colors.
Rule 1 — Color Contradiction: If two cells of the same color see each other (share a house), that color is impossible everywhere. Eliminate the candidate from all cells of that color.
Rule 2 — Color Trap: If an uncolored cell sees both a Color A cell and a Color B cell, the candidate can be eliminated from that cell (one color must be true, so the cell is blocked either way).
Simple Coloring works on one digit at a time. Multi-Coloring extends this with separate color clusters.
Examples
Simple Coloring on Digit 7 — Color Trap
Digit 7 forms conjugate pairs. Color chain: R0C2=Blue (pair in row 0), R0C6=Green (pair in row 0), R3C6=Blue (pair in col 6), R3C2=Green (pair in row 3), R8C2=Blue (pair in col 2). Cell R8C6 is uncolored and sees R0C6 (Green, same col 6) and R8C2 (Blue, same row 8). One of Blue/Green must be true, so R8C6 cannot be 7.
Pro Tips
- •Focus on one digit at a time — whichever has the most conjugate pairs
- •A conjugate pair means exactly two cells hold the candidate in a house
- •Follow the chain carefully: each link flips the color
- •Color Contradiction (same color sees itself) is the strongest result — entire color is eliminated
- •Color Trap (uncolored cell sees both colors) is more common and still very useful
