Contradiction

Extreme Used by Smart Hint

Suppose the cell were rejected (or kept) and follow the consequences — if the rules break, the opposite must be true.

Cells that establish the pattern

How it works

When no direct rule settles a cell, suppose an answer and follow it: imagine the highlighted cell is rejected, and apply the ordinary techniques from there.
If that supposition ends up breaking a rule — two rejected cells touching, a duplicate kept, or the board cut in two — the supposition was wrong.
The cell must then be the opposite of what you supposed. This is the last-resort technique: try the direct ones first.