Interactive Sudoku Technique
Coloring: Let Color Remember the Chain
Choose one candidate digit and follow its conjugate pairs across the grid. Two alternating colors preserve the chain’s either-or truth states so your eyes do not have to remember them. A conflict can disprove one color; an outside candidate caught by both colors can be removed. Multi-Coloring extends the same bookkeeping to separate networks.
The Idea You Were Reaching For
Color Records a Logical State
Your instinct is exactly right: remote cells can correspond to one another through a chain, and color lets the solver keep track of that relationship at a glance. The precise starting structure determines the technique’s name.
Repeated BVCs: Remote Pairs
Several remote cells all contain the same two candidates. Their two possible cell values alternate through shared houses. Coloring can help track that BVC chain.
One Digit: Simple Coloring
One selected candidate travels through conjugate pairs in rows, columns, and boxes. The colored objects are candidate positions for that digit, not entire BVC states.
Coloring is not a new Sudoku rule. It is visible bookkeeping for a chain of opposite truth states.
Begin with Exactly Two Places
A Conjugate Pair Supplies the First Two Colors
Filter the grid to one digit. When that digit has exactly two candidate positions in a row, column, or box, those positions form a conjugate pair. One must contain the digit and the other must not. This is the Strong Link that starts the color network.
The hues are names, not answers
Amber does not mean true and blue does not mean false. They mean “State One” and “State Two” until the grid proves which state survives.
The color belongs to one candidate
If a whole cell is shaded by the Sudoku Paradise tool, read the shade as applying only to the digit currently being traced. Other candidates in that cell are not assigned the same state.
The link color is a different language
On the AIC page, amber and blue lines identify inference types. Here, neutral lines connect conjugates while amber and blue fills identify opposite candidate states.
Propagate the Either-Or
Paint One Connected Network
Give the first conjugate pair opposite colors. Whenever a colored candidate has another conjugate partner, give that partner the opposite color. Continue until no new conjugate can be reached.
Start with either end of any conjugate pair. The first color is arbitrary.
Two Ways the Network Pays Off
Color Trap and Color Wrap
Rule One
Color Trap: An Outside Candidate Sees Both Colors
An uncolored candidate that sees an amber member and a blue member of the same network cannot be true. One color state or the other must supply the digit.
Test both possible states of the network.
In either state, a visible 7 defeats r4c2#7.
Remove 7 from r4c2.
Rule Two
Color Wrap: One Color Contradicts Itself
If two candidates of the same color see each other, that color cannot be the true state. Otherwise the house would contain the chosen digit twice. Remove every candidate of the failed color; the opposite color is true.
The two amber peers cannot both contain the digit.
Trap: an uncolored candidate sees both colors. Wrap: one color sees itself.
When One Digit Forms Separate Islands
Multi-Coloring Compares Disconnected Networks
Sometimes the same digit forms two or more conjugate networks that cannot be reached from one another by Strong Links. Each network still has two opposite states, but its orientation is independent. The first network needs one pair of identities; the second needs another.
1. Find the cross-network conflict
Suppose an A1 candidate sees a B1 candidate. They cannot both contain the digit, so at least one of their opposite states—A2 or B2—must be true.
2. Test the complementary states
Any outside candidate that sees an A2 and a B2 is defeated in every permitted relationship between the networks.
The two color pairs are internally valid but initially independent.
A second Multi-Coloring outcome
If candidates of one state in Network A collectively see both opposite states of Network B, then that state of Network A must be false. Network B must choose one of its states, and either choice defeats the same A state. This is the multi-network counterpart of a Color Wrap.
Use the Sudoku Paradise Color Tool Deliberately
A Reliable Coloring Routine
1. Choose one digit
Highlight every remaining position for that digit. Coloring several digits at once belongs to a different kind of chain.
2. Start with a conjugate
Find a house with exactly two positions. Give them opposite colors, then propagate only through other exact pairs.
3. Scan before expanding
Check for a same-color conflict first, then inspect every uncolored candidate that sees both colors.
4. Label separate components
If another network cannot be reached, give it its own pair identity. That is the doorway to Multi-Coloring.
Before accepting an elimination
- Every propagation step comes from an exact conjugate pair.
- Every connected pair receives opposite colors.
- The deduction concerns only the digit being colored.
- A Color Trap victim sees both states of the same connected network.
- A Multi-Coloring deduction first proves how the separate networks interact.
Read the Colors as Logic
Four Quick Coloring Decisions
Start the network
What permits two positions to receive opposite colors?
Read a Color Trap
An outside 6 sees amber 6 and blue 6 in one network. What follows?
Read a Color Wrap
Two amber 4s in one network see each other. Which state fails?
Keep components honest
Two disconnected networks use similar-looking colors. Are their states automatically synchronized?
0 of 4 decisions confirmed
Questions Worth Asking
Coloring Frequently Asked Questions
Does Simple Coloring require Bivalue Cells?
No. Simple Coloring follows one digit through conjugate pairs in houses. A colored cell may contain two candidates, three candidates, or more. Only the selected candidate’s position is carrying the color state.
Is a chain of repeated BVCs still a coloring idea?
It uses the same visual bookkeeping, but its recognizable technique is Remote Pairs: the two values of identical BVCs alternate across shared houses. Simple Coloring instead follows one candidate digit through conjugate pairs.
Does one color always mean true?
No. Before a contradiction is found, either color may be the true state. The names and hues can be swapped without changing the proof.
Is Coloring a form of guessing?
No. Both color states are preserved until the grid produces a conclusion valid under either state or disproves one state outright. No branch is chosen by preference.
Why can’t I reuse one color pair across every disconnected network?
Each disconnected network has its own independent either-or choice. Reusing a color name without a component label falsely claims that their truth states are synchronized. Multi-Coloring earns a relationship only when candidates from the networks see one another.
How does Coloring relate to an X-Chain?
Both reason about one candidate digit through the grid. Coloring displays connected conjugate states all at once; an X-Chain writes a particular alternating inference path. Color is often the easier human bookkeeping system.
Turn a Scattered Digit into a Truth Map
Filter One Digit, Then Let the Colors Talk
Begin with an exact pair, alternate the states, and never decide which color is true prematurely. First look for a color that contradicts itself. Then look for an outside candidate trapped by both states. If separate networks remain, label them independently before comparing them.