Multi-Coloring
Two separate colouring components for one digit collide, forcing their opposite colours and removing shared targets.
What it is
Multi-Coloring extends simple colouring to two independent conjugate-pair components for the same digit. Each component alternates two colours along strong links. If a cell of colour A in one component sees a colour-A cell in the other, those two candidates cannot both be true. Therefore the opposite colour must be true in one component, and a candidate that sees every opposite-colour cell in both components is impossible.
How to spot it
Build two separate strong-link colour chains for one digit. Keep the components separate: do not join them merely because cells see each other. Then look for equally coloured cells, one from each component, that see each other. Finally check outside candidates of the same digit that see all opposite-colour cells in both components.
Worked example
Step through the reasoning below. Each step adds one layer: first the position, then the pattern, then the candidates involved, and finally what can be eliminated.
Step 1 of 4: The starting position
- Pattern cells
- 1/2, 1/3, 4/2, 4/3, 4/8, 4/9, 5/8
- Digits
- 5
- Eliminations
- 4/9
Press a marked square to point it out on the board above.
Why it matters
Multi-Coloring turns two short colouring structures into a controlled contradiction. It finds eliminations that simple colouring misses while keeping the proof readable: every coloured edge is a conjugate pair and the one cross-component conflict is visible on the board.
Practise now
Solve a puzzle where this technique decides the game
Frequently asked questions
How is Multi-Coloring different from simple colouring?
Simple colouring works inside one connected conjugate graph. Multi-Coloring uses two separate graphs for the same digit and extracts a conclusion only when equal colours across the graphs see each other.
What makes a colour link strong?
A strong colour link comes from a conjugate pair: exactly two cells in one row, column or box can hold the digit. If one is false, the other must be true.
Can I remove every candidate sharing a unit with the conflict?
No. Only an outside candidate that sees every opposite-colour occurrence in both components is forced out. Sudoku Luna marks and verifies that complete target set automatically.
Put it to use
Where you will meet it
Expert grids are the only place this pattern regularly decides the solve. Bring your notes.
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