Solving The Locker Problem

 

First, I try to decipher the probelm by creating a table with the locker numbers and the student numbers up to 10.  By the time I finish the number 10, I can start to see a pattern. 

Numbers 1, 4, 9 have CLOSED lockers, and they are perfect square numbers.

Numbers 2, 3,5,6,7,8,10 have OPEN lockers. I can see that 2,3,5,7 are prime numbers, and 6,8,10 are even numbers. I begin to wonder what is in common between these two sets of numbers. Then, I notice that they both have even number of factors. As I go back to look at the Prime numbers,  I notice that they have odd number of factors. From there, I can conclude that, locker numbers with odd number of factors are CLOSED, and locker numbers with even number of factors are OPEN. 

Note that the first locker is remains CLOSED.