Coloring

What Is a Strong Link?

A strong link (conjugate pair) exists when a digit appears as a candidate in exactly two cells within a house. One must hold the digit, the other cannot. This binary relationship is the foundation of all coloring.

Simple Coloring: Single Digit Coloring

Operates on one digit at a time. Assign alternating colors through conjugate pairs using BFS. One color group is entirely true, the other entirely false. Level 5 (Challenging).

Color Trap and Color Wrap

Color Trap: An uncolored cell seeing both colors cannot contain the digit. Color Wrap: Two same-color cells sharing a house is a contradiction. That entire color is false; the other color is confirmed true.

3D Medusa Coloring: Multi-Digit Coloring

Extends coloring across multiple digits using bivalue cell links. A bivalue cell's two candidates get opposite colors. This creates a three-dimensional web of implications. Level 12 (Extreme).

Medusa Elimination Rules

Rule 1: Color Wrap (same as simple coloring, but multi-digit scope). Rule 2: Color Trap (same as simple coloring, multi-digit scope). Rule 3: Same Cell, Same Color -- two digits with matching colors in one cell means that color is false everywhere. Rule 4: Two Colors in a Cell -- a cell with both colors eliminates all uncolored candidates.

Simple Coloring vs. Medusa Coloring

Simple Coloring: one digit, faster, Level 5. Medusa: multiple digits, more powerful, Level 12. Medusa subsumes simple coloring but is much harder to apply manually. Learn simple coloring first.

How Coloring Fits into the Technique Hierarchy

Coloring introduces the idea of building logical arguments across the entire grid. Simple coloring is related to X-Chains. Medusa coloring is related to AICs. Learning coloring prepares you for all chain-based reasoning.

Summary

Simple Coloring (Level 5) uses conjugate pairs for a single digit with Color Trap and Color Wrap rules. 3D Medusa (Level 12) extends across multiple digits through bivalue cells, adding Same Cell Same Color and Two Colors in a Cell rules.