Simple Coloring in Sudoku: Marking Two Candidate Chains

Simple coloring follows one digit through a network of strong links. Alternating colors represent the two possible ways the chain can satisfy its units.

The technique is a visual aid for a logical contradiction, not a licence to colour every candidate on the board.

Choose one digit and a seed link

Find a unit where the digit has exactly two positions and color one candidate A and the other B. Continue only through strong links for that same digit.

Alternate at every link

When a unit offers exactly two positions, the colors must alternate. A connected chain therefore carries one of two consistent states: all A candidates are true, or all B candidates are true.

Find a color conflict

If two candidates of the same color see each other, that color cannot be true; remove all candidates of that color in the chain. The contradiction is that one unit would otherwise contain the digit twice.

Find a shared peer

A candidate that sees both colors cannot be true, because whichever color is selected one endpoint would occupy the relevant relationship. Remove it from that common peer.

Keep coloring local

Stop when the chain becomes hard to verify. Mark only one digit and audit every link. A small correct coloring is more useful than a large uncertain web.