Simple Coloring

Track Candidates Through Strong Links

By Minimal Sudoku Team•Last updated: February 6, 2026

Simple Coloring is a powerful technique that tracks a single digit through strong-link chains using two colors. When the two opposing colors create a contradiction or trap, you can eliminate candidates or place digits.

Quick Summary

What: Track one digit through strong-link chains
Colors: Two alternating colors represent either/or positions
Results: Find contradictions (eliminate one color) or traps (cells seen by both colors)
Difficulty: Advanced — requires understanding strong links

The Concept

Simple Coloring focuses on one digit at a time. For that digit, we find cells connected by strong links and alternate two colors through the chain. If one color is TRUE, the other is FALSE.

By tracing these chains, we can find:

Two cells of the same color that see each other (contradiction)
An uncolored cell that sees both colors (can be eliminated)

The Golden Rule

🎨 Simple Coloring Rule

Build an alternating two-color chain on one digit using strong links. Then apply two outcomes: eliminate a color if it contradicts itself in one unit, or eliminate any uncolored candidate that sees both colors.

Understanding Strong Links

🔗 Strong Link Definition

A strong link exists between two cells when they are the only two cells in a unit (row, column, or box) that contain a specific candidate. If one is FALSE, the other must be TRUE.

You may also see Simple Coloring referred to as Single's Chains.

Strong link visualization (digit 4):

In column 2, candidate 4 is locked to R2C2 and R5C2. If one is false, the other must be true.

How to Find Coloring Moves

Choose a digit

Pick a candidate to analyze. Digits appearing in 8–14 cells work well.

Find strong links

Identify all strong links for this digit — cells where the digit appears exactly twice in a unit.

Start coloring

Pick any cell in a strong link and color it BLUE. Color the other end GREEN.

Extend the chain

Follow additional strong links, alternating BLUE and GREEN through the chain.

Look for patterns

Check for contradictions (same color seeing itself) or traps (an uncolored candidate seeing both colors).

Practical Example

Simple Coloring on Digit 4

Simple Coloring example with candidate 4 elimination at R5C8

In this grid, candidate 4 forms strong links including:

In column 2, 4 can only go in R2C2 and R5C2.
In row 1, 4 can only go in R1C3 and R1C8.

The cell R5C8 sees both opposing chain ends R5C2 and R1C8.

Through the intervening strong links shown in the diagram, R5C2 and R1C8 are opposite colors in the same chain.

Elimination

Candidate 4 at R5C8 can see two opposing candidates in the chain (R5C2 and R1C8), so it can be eliminated.

Why It Works

Simple Coloring relies on alternating truth values across strong links:

One color is true, and the opposite color is false.
If the same color appears twice in one row, column, or box, that color is impossible everywhere in that chain.
If an uncolored candidate sees both colors, it is impossible regardless of which color ends up true.

Either/Or Logic

In the example, R5C8 sees R5C2 and R1C8, which are opposite colors. One of those two must be true, so 4 at R5C8 is impossible in every case.

Detection Tips

Start with Conjugate Pairs

Look for units with exactly 2 cells containing your target digit. These are your strong links — the building blocks of coloring.

Favor Short Chains First

Start with short, high-confidence chains around one box and one line. This keeps the either/or logic easier to verify.

Check All Chains

A grid may have multiple disconnected chains for the same digit. Analyze each chain separately and check for traps both within and across chains.

Only Strong Links

Simple Coloring uses ONLY strong links. If a unit has 3+ cells with the candidate, there's no strong link there — skip it for this technique.

Simple Coloring is the foundation for more advanced chain techniques:

When a coloring chain closes into a loop, the interpretation overlaps with X-Cycle logic (and can be viewed as a nice-loop style pattern in AIC terms).

Chain Techniques

🔄X-Cycle 🐍3D Medusa 🔗XY-Chain

Expert

X-Cycle

Extend coloring to include weak links for even more powerful deductions.

Related Advanced Techniques

✈️X-Wing 🗡️Swordfish 🦋Y-Wing