The Locker Problem
There are 100 students and 100 lockers in a certain school, each student has a certain locker number. The students and the lockers are uniquely numbered from 1 to 100. The students had a certain game. Initially, the lockers are all closed. The first student opened all the lockers. The second student closed every second locker.The third student opened or closed every third locker.This method goes until the 100th student. After all the students finish opening and closing the lockers, how many lockers are left opened ? and what are the lockers which are left opened ?