You are in a room, with 100 lights, and 100 dwarfs. The lights and the dwarfs are both numbered 1 through 100. The lights have one on/off switch, and in the beginning, they are all set to off. Then, every dwarf, passes through all the lights, touching the switch of the lights if and only if his (dwarf's) number divides the light's number.
In other words, dwarf number 1 turns on all the light, dwarf number 2 turns off the lights 2, 4, ..., 100, dwarf number 3 switches the lights 3, 6, ..., 99, turning some off and some on, and so forth.
After dwarf number 100 touches light number 100, the cycle finishes. At this point, which lights will be left on?