Sometimes psychic debugging consists merely of seeing the bigger picture.

On one of our internal bug-reporting mailing lists, someone asked, "How come when I do XYZ, my CPU usage goes to 50%?"

My psychic answer: "Because you have two processors."

The response was genuine surprise and amazement. How did I know they had two processors? Simple: If they had only one processor, the CPU usage would be 100%. This seems unhelpful on its face, but it actually does help diagnose the problem, because now they can search the bug database for bugs in the XYZ feature tagged "100% CPU" to see if any of those apply to their situation. (And in this case, it turns out that one did.)