In a row, there are 81 rooms, whose door no. are 1,2,.......,81, initially all the door are closed. A person takes 81 round of the row, numbers as 1 st round, 2 nd round ........ 81 th round. In each round, he interchage the position of those door number, whose number is multiple of the round number. Find out after 81 st round,How many doors will be open.
Text Solution
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9
Sol. Here, we note the following.
1. A door will open if it face odd number of changes.
2. Number of changes faced by any door will be equal to number of factors of the door number
3. So only those door will open, whose number is perfect square so ans is 
, [where [ ] denotes the G.I.F.]
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