The Locker Problem

My rough work for the locker problem.

 Explanation of my work:

I first tested a small sample set of 5 lockers and 5 students to see what the result would look like. Then I increased it to 6 to test to see if odd/even number of students/lockers made any difference (it did not). I noticed the C-O-O pattern (C for closed, O for open) was repeating so to test that, I tried a larger sample of 10. It did not repeat the C-O-O pattern but at this point, I realized that factors must be playing a role and made a list of factors for 1 to 10. I noticed that an odd number of factors closed lockers while even opened them. Finally, this led me to figuring out that odd number of factors occur on perfect squares because there is one "non-paired" factor (the squared factor). Thus, the lockers corresponding to perfect squares would be closed while the rest would be open.

The locker problem was really fun and made me use various skills/concepts, such as recognizing patterns and using knowledge about factors, to solve it.