Imagine there are a thousand lockers. A student because of he is bored tried open all the lockers. Then reverse state of the locker (open to close, close to open) every 2 lockers, then 3 and so forth until he does it for the 1000th time. find how many lockers are open.

Question

bahrom7893 · Answer

This one looks familiar actually

bahrom7893 · Answer

The only difference was 1000 students open and close in a row, but i think the solution's the same

anonymous · Answer

so whats the answer then?

bahrom7893 · Answer

is it 31?

anonymous · Answer

nope but i think you get the idea.

anonymous · Answer

yeah i started with close sorry. its 31.

bahrom7893 · Answer

Ok suppose we're talking about n lockers.

bahrom7893 · Answer

If the student a opens locker n, then it will also be opened by a student n/a.

bahrom7893 · Answer

I'm assuming there are 1000 students instead of one, but same idea, i could say if the student opens locker n on the ath turn, he'd reopen it later on (n/a)th turn. So now we have a = n/a, or n = a*a, where n is the number of the open locker.

bahrom7893 · Answer

So now we just have to find squares under 1000. lol I tried 32 - went above 1000 (1024 actually), but 31 works

anonymous · Answer

yeah i thought that i started with opened all then closed all so the answer on that scenario is 1000 - 31. XD