Question 8
There are 500 lockers numbered 1 to 500. Also, there are 500 students coming to the locker room. The first student opens all the 500 lockers. The second student then closes every locker with an even number, i.e. 2, 4, 6,... The third student then ‘reverses’ every third locker, i.e. if the locker is open, he/she will close it; but if the locker is closed, he/she will open it. The fourth student then ‘reverses’ every fourth locker, and so on until the 500ᵗʰ student has ‘reversed’ the 500ᵗʰ locker. What is the locker with the largest number that will remain open in the end?