Now teaching and studying is interesting
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.
The answer is 35.
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1 solution
The doors which are square numbered are left opened. that is 1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400,441,484,529,576,625,676,729,784,841,900,961. then the hundredth child does his duty. so the doors closed are 100,400,900,1000. So the number of doors left opened are 35.