Simple Coloring

Level 9 · Purple Belt

Strategy:

Requires:

Learn after:

Medusa Coloring Remote Pairs X-Cycles

Overview

Simple Coloring (Singles Chains) uses two colors to track conjugate pairs of a single digit. By alternating colors along chains, contradictions or eliminations can be found.

How It Works

Find conjugate pairs for a digit (exactly 2 occurrences in a unit).
Color one cell, give the opposite color to its conjugate.
Continue coloring along all connected conjugate pairs.
Rule 1 (Color Wrap): Same color twice in a unit - that color is false.
Rule 2 (Color Trap): Uncolored cell sees both colors - eliminate that candidate.

Example

Starting position

Look for Simple Coloring.

Sudoku grid showing the initial puzzle state for Look for Simple Coloring.

1

Build the coloring chain for 5

Build a coloring chain for digit 5 by following conjugate pairs.

Sudoku grid illustrating step 1: Build the coloring chain for 5 — Build a coloring chain for digit 5 by following conjugate pairs.

2

Colors alternate along the chain

Each link alternates color: exactly one color is true and the other is false.

Sudoku grid illustrating step 2: Colors alternate along the chain — Each link alternates color: exactly one color is true and the other is false.

3

Look for cells seeing both colors

Find uncolored cells that can see cells of both colors.

Sudoku grid illustrating step 3: Look for cells seeing both colors — Find uncolored cells that can see cells of both colors.

4

These cells always see a true 5

One color must be true, so every highlighted cell already sees a true 5 somewhere in the chain.

Sudoku grid illustrating step 4: These cells always see a true 5 — One color must be true, so every highlighted cell already sees a true 5 somewhere in the chain.

5

Remove 5 from trapped cells

Remove 5 from the cells that see both colors: r7c8.

Sudoku grid illustrating step 5: Remove 5 from trapped cells — Remove 5 from the cells that see both colors: r7c8.

6

Result

Result after applying the technique.

Sudoku grid showing the result after applying the technique

Tips & Patterns

Start from any conjugate pair and alternate colors systematically.
Either all cells of one color are true, or all cells of the other color are true.
Color Trap is the most common elimination type.