Now teaching and studying is interestingNumber Theory Level 3
In a huge colony the parents, to improve the math skills of all their children decide to teach them in an interesting way and this is one of those attempts. There were 1000 doors numbered 1,2,3.... so on and 1000 children. The first child was asked to open all the doors. Then they asked the second child go to every second door and close it. The third goes to every third door and, if it is closed, he opens it, and if it is open, he closes it. The fourth child does this to every fourth door, and so on. The process continues until the thousandth child has done his job. Then the 100th child repeats his job again. Find the number of doors which are finally open.