Riddles, brain puzzles and mathematical problems

[Froge]

Can this puzzle even be solved?

Case 1: All switches off. The room is dark. The one that controls the bulb could be any of the three.
Case 2: Turn on one switch. If the room is light, then that switch must be the correct one. If the room is dark, it's either of the other two.
Case 3: Turn on two switches. If the room is dark, then the last switch must be the correct one. If the room is light, then the correct switch must be either of the two you just turned on.
Case 4: Turn on all switches. The room is light. The one that controls the bulb could be any of the three.

Cases 1 and 4 as well as 2 and 3 are reflections of each other (in terms of light/dark). 1 and 4 are useless, while cases 2 and 3 gives you a half chance of guessing the correct switch if it is dark or light respectively. Because we can't enter the room twice, I don't see how the puzzle could be solved.