TECHNIQUE · EXPERT
Coloring — chain a digit's conjugate pairs
When a digit has exactly two candidate cells in a unit, those cells form a conjugate pair. Paint them with two colors and chain the pairs together — contradictions eliminate an entire color, and cells that see both colors cannot hold the digit.
The logic
Exactly one cell of a conjugate pair holds the digit. Painting the pair with colors A and B propagates a binary choice along chained pairs. If color A appears twice in one unit, color A is impossible everywhere; if a cell sees both colors, it cannot hold the digit regardless of which color is true.
How to find it
For one digit, locate every unit (row, column, or box) where the digit has exactly two candidates. Paint the pair with alternating colors and extend the chain through shared cells.
- Pick a digit with many remaining candidate cells.
- For each unit, find conjugate pairs (digit has only two candidate cells).
- Paint the two cells of each pair with colors A and B alternately.
- If one color appears twice in any unit, remove the digit from every cell of that color.
- Remove the digit from any cell that sees both colors.
Gateway to advanced chains
Coloring is the foundation of Forcing Chains and X-Cycles. Once single-digit chain reasoning feels natural, multi-digit chain techniques become much easier to read.
Practice order
- Pick a digitChoose an unplaced digit with several candidate cells.
- Find conjugate pairsLocate every unit where the digit has only two candidates.
- Two-color paintAlternate colors A and B across each pair's two cells.
- Contradiction or double visionWatch for a color appearing twice in one unit or cells seeing both colors.
Walk through Coloring
Step 1 of 4
Focus on digit 7. In row 1, the only two candidate cells for 7 are (row 1, col 1) and (row 1, col 4) — the first conjugate pair.