Originally Posted by

**Nefertari**
No, I don't mean ANY number above 1005 would be left untouched.

I mean by the time we progressed to beyond say 1004th student, some lights beyond this point will have been switched off and then on at least once, most will experienced this just once, and factors beyond this point will be on. My guess is that the off lights at this point will be a lot less than the on lights. So, keeping this in mind, as the multiples keep progressing, the majority of the lights which are previously on will in the end be off.

For example, say from 1010 to 1020, if 1011, 1013, 1014, 1015, 1017, 1019, 1020 are still on by then, they will all be off eventually as the 1010th to 1020th students will switch them off. Conversely, 1012, 1016 and 1018 will be turned on. So, we can see, the proportion of 'off' lights are much more than 'on' lights. The answer can't be 1005, but I'm not sure how many. But I guess it'd be reasonable to say, the answer would be between 30 and 150?

Also, all factors (2,3,5,7 .....) will eventually be off. The first light will always be on.