Simple Coloring in Sudoku, Step by Step

The idea behind coloring

Coloring works on one digit at a time. In many units that digit has only two possible cells left. Those two cells form a conjugate pair, meaning exactly one of them is the digit and the other is not. If you color one cell, the other must be the opposite color. Chaining these pairs across the board splits many cells into two groups, and within each chain the two colors are perfect opposites.

Building the chain

1. Pick a digit and find every unit where it has exactly two candidate cells.
2. Start at one cell, give it color A, and give its partner color B.
3. Follow the links. Every time a colored cell shares a conjugate pair, the partner gets the opposite color.
4. Keep going until the chain stops growing.

The two ways it pays off

There are two conclusions. First, if two cells of the same color sit in the same unit, that color must be false, because a unit cannot hold the digit twice. So every cell of the other color becomes the digit. Second, and more common, any uncolored cell that can see both a color A cell and a color B cell cannot be the digit at all, since one of those two colors is the true one. You erase the digit from that cell.

Why it is worth learning

Coloring reaches eliminations that pairs and fish miss, and it needs nothing more than two highlighters or two note colors. Start with digits that appear as tidy conjugate pairs in several units, since those chains grow the fastest and reveal the most.