The Locker Problem

After reading this problem, I tried to visualize it. Since it is not reasonable for me to visualize 1000 lockers at once, I decided to start by looking at only the first 10 lockers. After drawing it out and summarizing the findings, I tried to find a pattern. So far, the perfect squares less than 10 remain closed. I would try to test this by observing the next 10 lockers to see if this pattern holds. If it does, then the lockers that would remain closed would be {1,4,9,16}.