Platon Sudoku · Sudoku Study

Multi-Component Coloring Contradiction · Step-by-step example

Strong links color one digit into opposite states within each component; relationships between components constrain which states can coexist. Remove a candidate excluded by all consistent color assignments.

This course is adapted from Platon Sudoku App. Read the complete example here, then continue learning and practising in the app.

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Recognize the pattern

Strong links color one digit into opposite states within each component; relationships between components constrain which states can coexist.

How to find it

Color each connected component separately, then inspect cross-component conflicts and targets that see every surviving alternative.

What it allows

Remove a candidate excluded by all consistent color assignments.

Avoid the mix-up

Do not join separate components with an unverified strong link or assume a color is already placed.

Step-by-step example · Complex color

This example starts from a saved intermediate position. Its candidates include earlier logical eliminations; they are not fresh automatic notes.

Blue: evidence. Green: conclusion. Crossed-out digits: eliminated candidates. R1C1 means row 1, column 1.

Step 1 · Confirm the starting same-state group

“Multi-Component Coloring Contradiction” is this app’s descriptive name for a custom multi-component proof, not a separate same-named HoDoKu technique. Candidate 2 forms 4 separate coloring components. Alternating along the strong links puts R3C1=2, R8C2=2 together on side A of component 2, so these members share one truth state. They are exactly the target candidates R3C1=2, R8C2=2. Within each component, A and B are opposite states; conflicts link states across components.

● 1A: R1C2=2

■ 1B: R1C9=2

● 2A: R3C1=2, R8C2=2

■ 2B: R8C1=2

● 3A: R3C4=2

■ 3B: R4C4=2

● 4A: R4C7=2, R5C6=2

■ 4B: R5C9=2

Step 2 · Assume the target state is true

Treat the whole same-state group R3C1=2, R8C2=2 as one state and temporarily assume it is true. Follow the conflicts between components.

Step 3 · Follow every component transition

1. R3C1=2 is true, so the visible peer R1C2=2 is false. The opposite A/B state R1C9=2 in that group is therefore true. 2. R1C9=2 is true, so the visible peer R5C9=2 is false. The opposite A/B state R4C7=2, R5C6=2 in that group is therefore true. 3. R4C7=2 is true, so the visible peer R4C4=2 is false. The opposite A/B state R3C4=2 in that group is therefore true. 4. R3C4=2 is true, so the visible peer R3C1=2 is false. The opposite A/B state R8C1=2 in that group is therefore true.

Step 4 · The assumption forces its opposite

The assumption R3C1=2, R8C2=2 eventually forces R8C1=2, the opposite A/B state in the same group. Both states cannot be true, so the assumption is false.