Because at most two of the same color immediately next to or below each other are allowed, pairs can be filled in with the other color. Thus, in the example to the right, both pink cells should be white.
Similarly, the blue cell should be black to prevent three white adjoining cells.

Each row and each column should contain an equal number of colored cells. Therfore the blue cell must be black and the pink one white.

Each row and each column must be unique.
Therfore the blue cell must be black and the pink one white.

There are two more blacks and one white for the row.
But the blue cell cannot be the last white because that would leave three consecutive blacks. Therefore the blue cell is black.

Again there are two more blacks and one white for the row.
But the blue cell cannot be the last white because that would make the row a duplicate of the first row. Therefore the blue cell must be black.
These patterns occur in the hard puzzles.