Following recess, the 1000 students of a school lined up and entered the school as follows: The first student opened all of the 1000 lockers in the school. The second student closed all lockers with even numbers. The third student “changed” all lockers that were numbered with multiples of 3 by closing those that were open and opening those that were closed. The fourth student changed each locker whose number was a multiple of 4 and so on. After all 100 students had entered the building in this fashion, which lockers were left open?