There are 100 lockers at Ridgemont high school. On their first day, the students see that all the 100 lockers are open. The students come up with a game. Each student opens or closes the lockers. The first student shuts every locker that's a multiple of 2. Then the next student closes every door that's a multiple of 3 unless its currently closed, in which case the student opens it back up. This continues, with the k-th student changing the state of all the lockers that are multiples of the k-th prime number.