Student Locker Problem
There are 2000 lockers and 2000 students. Their teacher assigns them a task. First student goes and opens all the lockers. Second student goes and closes every second locker. Similarly third student goes and opens every third locker if it is closed and closes it if it is open and so on. What is the number of open lockers after each student has performed his task ?
The answer is 44.
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1 solution
The locker with odd no. of factors will be left at the end i.e. the perfect square, thus until 2000, the biggest perfect square <= 2000 is, 1936 ( square of 44). Thus the answer is 44. :)