Lockers!
1000 students with numbers form 1 to 1000 are at a school and they each have a locker numbered 1 to 1000. All the lockers are closed at the start. If each student changes the state (closes if it is open or opens if it is closed) of all the lockers divisible by their number, how many lockers are left open at the end?
The answer is 31.
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1 solution
All the lockers that are open are the ones with an odd number of factors, and they can only be perfect squares. 31x31=961 and 32x32=1024, so there are 31 perfect squares under 1000, and hence the answer.