Coloring
For one candidate, colour the ends of conjugate pairs alternately and propagate. Contradictions in the colouring drive eliminations.
Candidate 9 forms a chain of conjugate pairs — alternate cells are colored opposite, since only one of each pair can be true.
How to spot it
- 1Find conjugate pairs for a digit and colour their ends opposite colours.
- 2Propagate the colours along connected pairs.
- 3Two same-colour cells in one house make that colour false; a cell seeing both colours loses the digit.
When to use
As a visual entry point to chain logic.
Common mistake
Colouring across a non-conjugate link, which breaks the logic.
Worked Example
Coloring tracks a single candidate across a network of conjugate pairs by assigning alternating "colors" to their ends — since exactly one cell in each conjugate pair is true, connected cells always get opposite colors. Following the connections across the grid builds up two color groups, one of which will turn out to be the real placements for that digit.
Two things reveal which: if two cells of the same color ever share a house, that color is impossible everywhere (a house can't hold the same digit twice), so every cell of the other color must be true instead. Separately, any cell outside the chain that sees one cell of each color can be eliminated regardless of which color wins, since one or the other is guaranteed to hold the digit. It's a visual way into the same logic that underlies formal chains.