Sometimes the only hint you need to solve a puzzle is that it can be solved without a hint.
Last week a colleague and I were staring in puzzlement at something weird in a terminal window. After 30 seconds I said "Oh! I've worked out why that happens!". Five seconds later, she got it too, because _now_ she knew that it was possible to get the answer without going off to do an hour of research, and that narrowed the search space of what the answer could possibly be.
And this week, I was puzzled by a compiler error message referring to a particular C++ header, so I went and looked in (one implementation of) that header to see what it did. I found it did nothing interesting, or magic, or tied in to the internals of the compiler, at all. And that was enough to make me figure out what was going on with the error message – again, because there just weren't that many options left.
When it happens, it feels like one of those deliberate puzzles in which Paul says "Ah, now I know what the numbers are!" and Sophie replies "Ah, in that case, so do I!" Only somehow reality managed to create the same effect by accident.