Build a chain of conjugate pairs for one digit and assign two alternating colors. Contradictions reveal the truth.
Also known as: Single-Digit Coloring, Singles Chains
Pick one digit and link its conjugate pairs — the digit's only two spots in a unit — into a chain, colouring alternately. One colour is true, the other false. Remove the digit from any cell outside the chain that sees both colours, and from every cell of a colour in which two cells see each other.
Simple Coloring is a single-digit technique that extends the idea of conjugate pairs into chains. For a chosen digit, you find cells that form conjugate pairs (the digit has exactly two candidates in their shared unit) and link them together. Each pair gets alternating colors, if one cell is green, the other must be blue.
The chain grows by connecting overlapping conjugate pairs. Once built, you have a network of cells where one entire color must be true (those cells contain the digit) and the other must be false. This binary constraint leads to two types of eliminations.
Color Trap: If a cell outside the chain can see cells of both colors, it cannot contain the digit, because one color is true, so one of those colored cells already has the digit. Color Wrap: If two cells of the same color see each other, that color is self-contradictory. The entire color is false, meaning every cell of that color does not contain the digit.
Pick a digit and find all conjugate pairs, units where the digit has exactly two candidate cells. Start at any cell, color it green. Its conjugate partner gets blue. If the blue cell has another conjugate partner in a different unit, that partner gets green. Continue alternating colors.
Once the chain is complete, check for Color Trap: scan each uncolored cell that has the digit as a candidate. If it can see (shares a unit with) both a green cell and a blue cell, eliminate the digit from that cell. One of those colors is true, so the digit is already placed in one of the visible colored cells.
Also check for Color Wrap: examine all cells of each color. If any two cells of the same color share a unit, that color contradicts itself, the same digit can't go in both. Eliminate the digit from ALL cells of that color. The opposite color cells must contain the digit.
Example 1: Color Trap
Step 1: Scanning digit 9, we build a chain of conjugate pairs — units where 9 has exactly two candidate cells. Colouring alternately along the chain gives green cells {R2C3, R6C6, R8C4} and blue cells {R6C3, R4C4, R9C6, R8C2}. One entire colour must be true.
Step 2: Cells R1C2 and R2C2 are NOT in the chain, but each can see a green cell (R2C3) and a blue cell (R8C2). Since one of those colours is true, a 9 already sits in a cell visible to both.
Step 3: Eliminate digit 9 from R1C2 and R2C2. Whichever colour turns out true, the 9 they can see is already placed.
Example 2: Color Wrap
Step 1: Scanning digit 6, we build a chain of conjugate pairs spanning 8 cells. We assign green and blue colors alternately through the chain.
Step 2: Two cells that were assigned the same color (let's say blue) turn out to see each other, they share a row or column. This means the blue color is self-contradictory: digit 6 can't go in both cells.
Step 3: Since blue is false, eliminate digit 6 from ALL blue cells. The green cells must contain 6. This often places the digit in multiple cells at once.
A conjugate pair is two cells that are the only candidates for one digit inside a unit — a row, column or box. Because the digit must go somewhere in that unit, one of those two cells holds it and the other does not. Simple Coloring chains these pairs together and colours them alternately.
A Colour Trap eliminates from outside the chain: an uncoloured cell that sees both a green and a blue cell loses the digit, since one colour is true. A Colour Wrap eliminates from inside: if two same-coloured cells see each other, that colour is false, so every cell of that colour loses the digit.
No — Simple Coloring works on a single digit at a time. Every cell in the chain is coloured for the same digit, and the colours say only whether that digit goes there. To use the technique on another digit you start again, building a fresh chain of that digit’s conjugate pairs.
Yes — within one connected chain, every cell of the surviving colour holds the digit. The two colours alternate along conjugate pairs, so they are exact opposites: if one is false, the other is true everywhere. That is why a Colour Wrap is so productive, placing the digit in several cells at once.
Both work on one digit, but an X-Wing needs a fixed shape: the digit confined to the same two columns in two different rows, forming a rectangle. Simple Coloring has no shape requirement — you follow conjugate pairs wherever they lead, so the chain can wander across the grid and be any length.
Traps are more common; wraps are more powerful. The everyday case is a Colour Trap — an uncoloured cell that happens to see both colours and loses the digit. A wrap needs two cells of the same colour to share a unit, which happens less often but clears the digit from every cell of that colour.
Explore all 28 solving techniques in our complete technique guide.