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
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.
Explore all 28 solving techniques in our complete technique guide.