The Locker Problem

Locker Problem

The locker problem was that there were 1000 lockers and each locker needed to be tested by being opened and shut. The first kid opened all the lockers then the second kid changed the state of every other locker then the third kid every three lockers etc…
After going through all the numbers we found there were 31 lockers open. Those specific lockers are open because they were changed the state of an odd number of times like open close open. Strangely all the open lockers are perfect squares like 1 4 9 16 ect... I think the perfect squares are all open because each perfect square goes up by an different odd number. More specifically every locker goes up by a higher odd number as shown in my diagram below. I think this effects why the lockers were open an odd number of times.