We need to know how to do this without having to open and close this many doors. There must be a way.

We don't need the answer, but a method of finding it would be wonderful.

On graduation day, 200 seniors line up outside the school. As they enter the school, they pass the school lockers, aptly numbered 1 to 200. The first student opens all of the lockers. The second student closes every other locker beginning with the second locker. The third student changes the status of every third locker beginning with the third one (if opened, the student closes it; if closed, the student opens it). The fourth student changes the status of every fourth locker. The fifth student changes the status of every fifth locker, and so on. Which lockers remain open after all 200 students have entered the school?

Use any method you want to solve the problem, but I MUST see all work and be given a short explanation of how you solved the problem.

4 extra credit points for the correct answer(s) AND a complete explanation of how the problem was solved.

Do you recognize a pattern? What is it? 2 extra credit points

4 extra credit points for being able to explain WHY the pattern exists.