15. There are 100 closed lockers in a hall, and 100 students. Student 1 walks down the hall and opens all 100 lockers. Student 2 closes all even-numbered lockers. Student 3 looks at every third locker (a multiple of 3), and if it is open closes it, or vice-versa (this student changes the condition of the locker). Student 4 repeats the action of student 3, but only changes the condition of lockers that are a multiple of 4. This goes on with every student doing the same routine for his or her number.