Advanced Sudoku Strategy
Simple Coloring Sudoku: How to Use Candidate Coloring
Learn how to follow strong links for one candidate, assign two alternating colors, and use contradictions or shared visibility to make logical eliminations.
One Candidate, Two Colors
Simple Coloring follows strong links for a single candidate and alternates two colors through the connected chain.
Find Strong Links
Look for a candidate that appears exactly twice in a row, column, or box.
Alternate Two Colors
Assign opposite colors to each end of a strong link and continue through connected links.
Find Eliminations
Use a color trap or color wrap to identify candidates that cannot be true.
What Is Simple Coloring in Sudoku?
Simple Coloring is an advanced Sudoku technique used to track the logical relationships between possible positions for one candidate.
Instead of looking at several different candidate numbers, you choose one candidate and follow its strong links through rows, columns, and boxes.
The connected candidate positions are assigned two alternating colors. You might think of them as Color A and Color B.
If Color A is true, every Color B position connected through the chain is false. If Color B is true, the opposite happens.
You do not need to know which color is true at the beginning. The relationship between the two colors is enough to find certain eliminations.
What Is a Strong Link?
Strong links are the foundation of Simple Coloring.
Exactly Two Possible Positions
Suppose candidate 7 can appear in exactly two cells in a row.
One of those two cells must eventually contain 7. If the first position is false, the second must be true, and vice versa.
This relationship is called a strong link.
Strong links can occur in a row, a column, or a 3×3 box.
What Is a Conjugate Pair?
When one candidate appears in exactly two cells within a Sudoku unit, those two positions are often called a conjugate pair.
Example
If candidate 5 appears only in R3C2 and R3C8 within row 3, then one of those cells must contain 5.
Simple Coloring connects several conjugate pairs to form a larger logical chain.
How the Two Colors Work
The colors are only visual labels. They do not represent specific numbers or predetermined true and false values.
Assign the first candidate position one color.
Assign the other end of the strong link the opposite color.
When another strong link continues from one of these positions, alternate the color again.
Every position with the same color represents the same truth state within that connected coloring chain.
How to Find Simple Coloring
Choose One Candidate
Select one number from 1 to 9 and examine all of its remaining candidate positions.
Find a Strong Link
Find a row, column, or box where your chosen candidate appears in exactly two cells.
Assign Two Colors
Give one end of the strong link Color A and the other end Color B.
Follow Connected Strong Links
From either colored candidate, check its row, column, and box for another strong link involving the same candidate.
Keep Alternating Colors
Each time you cross a strong link, switch to the opposite color.
Check for a Color Trap
Look for an uncolored candidate that can see both colors in the same chain.
Check for a Color Wrap
Check whether two candidates of the same color can see each other in a row, column, or box.
Make the Elimination
Apply the appropriate coloring rule and then rescan the puzzle for simpler solving opportunities.
Simple Coloring Rule 1: Color Trap
A color trap is one of the most useful Simple Coloring eliminations.
Suppose an uncolored candidate can see one Color A candidate and one Color B candidate from the same coloring chain.
Why Can It Be Removed?
One of the two colors must be true.
If Color A is true, the uncolored candidate is eliminated because it sees Color A.
If Color B is true, the same candidate is eliminated because it also sees Color B.
The uncolored candidate is impossible regardless of which color is true, so it can be removed.
Color Trap Example
Suppose you are coloring candidate 6.
If an uncolored candidate 6 can see both R2C3 and R7C8, it cannot remain.
Remove candidate 6 from that uncolored cell.
Simple Coloring Rule 2: Color Wrap
A color wrap occurs when two candidates with the same color can see each other.
For example, suppose two Color A candidate 4s appear in the same row.
Both Cannot Be True
A Sudoku row cannot contain the same number twice.
Therefore Color A cannot represent the true positions.
Every Color A candidate in that connected coloring chain is false and can be removed. The opposite color is therefore true within the chain.
Color Wrap Example
Suppose you have created a coloring chain for candidate 8.
Both Color A candidates appear in row 4, so they can see each other.
They cannot both be true.
Color A must be false. Remove all Color A candidate 8s from that connected coloring chain.
Where Can Strong Links Connect?
A Simple Coloring chain can move through different Sudoku units.
Rows
Two positions for one candidate in a row can form a strong link.
Columns
Two positions for one candidate in a column can continue the chain.
Boxes
A candidate restricted to two cells in a box can also create a strong link.
A useful coloring chain often moves from a row into a box, then into a column, and continues elsewhere in the grid.
Simple Coloring vs. Skyscraper
If you are learning strong-link patterns, our Skyscraper Sudoku guide is a useful technique to study alongside Simple Coloring.
Simple Coloring vs. X-Wing
For another single-candidate technique, review our X-Wing Sudoku guide .
Simple Coloring vs. XY-Wing
For a different advanced candidate pattern, continue with our XY-Wing Sudoku guide .
When Should You Look for Simple Coloring?
Many Strong Links
If one candidate has several conjugate pairs across the grid, it may create a useful coloring chain.
One Candidate Is Highly Restricted
A number with only a few possible positions in several rows, columns, or boxes is a good candidate for coloring.
After Simpler Techniques
Try singles, pairs, Locked Candidates, and simpler advanced patterns before building longer coloring chains.
In Hard or Expert Sudoku
Simple Coloring becomes especially useful when a difficult puzzle has stalled but still contains several strong links.
When Is It Not Simple Coloring?
❌ You Are Mixing Candidates
A Simple Coloring chain follows one candidate number only.
❌ A Link Has More Than Two Positions
If a candidate appears in three or more cells in a unit, those positions do not form the conjugate pair needed for that strong link.
❌ Colors Are Not Alternating
Each time you cross a strong link, the color must switch.
❌ An Elimination Sees Only One Color
For a color trap, an uncolored candidate must see both opposite colors from the same connected chain.
Common Simple Coloring Mistakes
❌ Coloring Every Candidate
Do not color every occurrence of a number. Follow only candidates connected through valid strong links.
❌ Treating the First Color as True
Color A and Color B are only labels. You do not initially know which color represents true candidates.
❌ Using a Weak Relationship as a Strong Link
The coloring chain must be built from units where the candidate has exactly two possible positions.
❌ Connecting Separate Color Chains
Do not assume colors from separate, unconnected chains represent the same truth state.
How to Practise Simple Coloring
1. Choose One Candidate
Start with a number that has relatively few possible positions remaining.
2. Mark Conjugate Pairs
Find every useful row, column, and box where that candidate appears exactly twice.
3. Build One Chain
Start with one strong link and follow connected links as far as possible.
4. Alternate Carefully
Check that every strong-link transition changes from one color to the other.
5. Search for Trap and Wrap
First look for uncolored candidates seeing both colors, then check whether same-colored candidates conflict.
6. Rescan After Every Elimination
A coloring elimination may reveal a single, pair, Locked Candidate, Skyscraper, or another advanced pattern.
Simple Coloring Practice Checklist
- 1. Are you tracking only one candidate?
- 2. Does each strong link have exactly two candidate positions in its unit?
- 3. Did you give the two ends of each strong link opposite colors?
- 4. Are all colored candidates part of the same connected chain?
- 5. Does an uncolored candidate see both colors for a color trap?
- 6. Do two same-colored candidates see each other for a color wrap?
- 7. Are you eliminating only the candidate being colored?
- 8. Did you avoid assuming one color was true before proving it?
- 9. Did you rescan the puzzle after the elimination?
Related Sudoku Learning Pages
🧠 Advanced Sudoku Techniques
Explore advanced strategies including pairs, fish patterns, wings, rectangles, strong links, and candidate chains.
🔒 Locked Candidates Sudoku
Learn how candidate restrictions between boxes and lines create useful eliminations.
✖️ X-Wing Sudoku
Learn a four-corner candidate pattern across two rows and two columns.
🔺 XY-Wing Sudoku
Use three bivalue cells to force a shared-candidate elimination.
🏙️ Skyscraper Sudoku
Use two strong links for one candidate to create roof-based eliminations.
▭ Unique Rectangle Sudoku
Learn how rectangle patterns can reveal eliminations based on puzzle uniqueness.
Frequently Asked Questions
What is Simple Coloring in Sudoku?
Simple Coloring follows strong links for one candidate and assigns alternating colors to the connected candidate positions. The color relationships can reveal contradictions and eliminations.
What is a strong link in Simple Coloring?
A strong link exists when a candidate appears in exactly two cells within a row, column, or box. One of those two positions must contain the candidate.
What is a color trap?
A color trap occurs when an uncolored candidate can see both opposite colors from the same coloring chain. Because one color must be true, the uncolored candidate can be eliminated.
What is a color wrap?
A color wrap occurs when two candidates with the same color can see each other. That creates a contradiction, so that color is false throughout the connected chain.
Does Simple Coloring use more than one candidate?
No. Simple Coloring follows one candidate number at a time through a network of strong links.
Is Simple Coloring an advanced Sudoku technique?
Yes. It is generally considered an advanced strategy and is particularly useful in Hard and Expert Sudoku puzzles.
Practise Simple Coloring
Open a Hard or Expert Sudoku puzzle, turn on Notes, choose one candidate, find its conjugate pairs, and follow connected strong links using two alternating colors.