This question already has an answer here:
- Nerds, Jocks, and Lockers 4 answers
You have a hundred, labeled, bulbs, turned off and a hundred, labeled, buttons.
When you begin pressing the button nº1, all bulbs turn on. When you then press the button nº2 all pair bulbs, begining by the 2n, turn off. When you press the button nº3, begining by the 3rd bulb, and all those which are multiples of 3, change their state. The ones that were off, light on, the ones turned of, go off.
You do the same by every button, finally having pressed, by order, all buttons from the first to the 100th. Question is, how many bulbs will be turned on at the end of the process? Which ones will it be?
As pointed out, this puzzle resembles Nerds, Jocks, and Lockers, being the question I asked a somehow simplyfied version of it. I'll leave the question as it is, in case anybody wants to try with this one. Of course, if that's not the case, I'll eventually end up closed.