Which bulbs will be lit and which ones will be switched off ?

Question

There are 100 bulbs in a room. 100 strangers have been accumulated in the adjacent room. The first one goes and lights up every bulb. The second one goes and switches off all the even numbered bulbs - second, fourth, sixth... and so on. The third one goes and reverses the current position of every third bulb (third, sixth, ninth� and so on.) i.e. if the bulb is lit, he switches it off and if the bulb is off, he switches it on. All the 100 strangers progresses in the similar fashion.

After the last person has done what he wanted, which bulbs will be lit and which ones will be switched off ?

Answer 1

All perfect squared bulbs will be ON, the rest will be OFF
Because they have odd number of factors,so they go from ON->OFF->ON...->ON
The bulbs will stay ON are: 1, 4, 9, 16, 25, 36, 49, 64, 81 & 100
The bulbs will stay OFF are the rest 90.