Forcing Chain

Take a cell with two candidates, assume the first, and follow the consequences as far as they go — every single that falls out, and every single those produce. Then start again and do the same with the second candidate.

Anything both branches arrive at must be true whichever candidate is right, so it can be placed without ever learning which one it was. If one branch reaches a contradiction, the other candidate is proved outright.

This is bifurcation: unlike every other technique here, it works by trying a value and seeing what happens rather than by proving something about the position directly. That makes it powerful and, to most solvers, unsatisfying — the answer arrives without a reason you could explain at the point you wrote it down.