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Q.> A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are 1000 lockers and 1000 students in the school. The principal asks the 1st student to go to every locker and open it. Then he has the 2nd student go to every 2nd locker and close it. The 3rd goes to every 3rd locker and, if it is closed, he opens it, and if it is open, he closes it. The 4th student does this to every 4th locker, and so on. After the process is completed with the 1000th student, how many lockers are open ?

Subham Sen
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    Hint: think of prime numbers ....how do they decisively affect this game? – DonAntonio Jan 24 '19 at 12:42
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    Welcome to Math StackExchange! Please describe what you have tried to solve the problem, so that the community can provide an answer relevant to you. – Swapnil Rustagi Jan 24 '19 at 12:42
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    An obvious way to start is to look at what happens to, say, the first $20$ lockers. Which of these are left open? Once you do that, I think the pattern will be clear. – lulu Jan 24 '19 at 12:48

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