Tier 2
Region containment
A colour trapped inside one row or column owns that line — every other colour has to leave it.
Look at a region and ask: which rows can its queen still occupy? If the answer is “only row 5”, then row 5’s queen is that colour’s queen. Nobody else gets it.
So every uncrossed square in row 5 belonging to a different colour can be crossed off — even squares that look completely unrelated to the region you were staring at.
The same argument runs column-wise. If a colour’s surviving squares all sit in column 2, then column 2 belongs to that colour.
An example worth walking through
Suppose the orange region has three squares left: (5, 2), (5, 6) and (5, 7). You do not know which one holds the queen, and it does not matter. All three are in row 5, so orange’s queen is in row 5, so row 5’s queen is orange. Every non-orange square in row 5 dies.
This is the first technique where you eliminate squares without knowing anything more about the region that caused the elimination. That shift — reasoning about a set of possibilities rather than a specific square — is what separates tier 1 from tier 2.
Do not stop at the obvious direction
The converse is a separate technique and it fires in different positions: row and column confinement starts from a line and concludes something about a colour. Both are worth checking on every pass; they are cheap.