Locker puzzle

1. A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:
There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?

Students and lockers are numbered 1 to 1000. Lockers will be opened/closed by students whose number is a factor of that locker number. Eg. Locker 16 will be opened by student 1, 2, 4, 8 and 16. For a locker to be open at the end of the process it would have to have an odd number of factors. As factors occur in pairs for most numbers the only ones with an odd number of factors are the perfect squares. ie 1, 4, 9, 16, 25 36 etc... So how many perfect squares less than 1000? (1,4,9,16,25,36,.......,900,961). 31²=961, 32²=1024.
So the answer is 31.