Then I believe this is written wrong because that is the solution. You can only enter once and all the switches have to start in the off position. Just out of curiosity then, what is the answer to the way this is written?

hmmm...Light is energy. And LED's do give off heat. Albeit not as much incandescent or fluorescent. Perhaps the update should include "and you have bankers hands because you have been counting money your whole life". - Quinn

Incandescent lighting has nothing to do with the answer, fluorescent lamps give off heat and that is the solution. Turn one switch on for several minutes, then turn it off and one more switch on. When you enter the room, one will on, one will be off, and one will hot to the touch