100 Door Puzzle Solution

To understand the solution let's take an example. let us take the door number 15. so 15 will divisors as 1&15 and 3&5. So after this pass it will come back to it's original position because 1 will open,3 will close,5 will open and 15 will close.So the door will remain in it's original state. But what about the door 25. it has 1&25 and 5&5 as it's divisors. But since 5 will occur only once so after all the passes 25 will be open. So this means that all those which are perfect squares will be open and rest will be closed.