I've got three strategies for solving problems:
In a whiteboard interview, "thinking about it" doesn't seem to work for me, because I think of all sorts of stupid things on the way to figuring something out.
"Trying things" depends a lot on the interviewer. Some seem to wonder why I'm trying something so obviously wrong. Also, whiteboard code isn't executable, so trying things looks like asking the interviewer for the answer.
Knowing the answer already thus the most sensible approach.