In a row there are 'n' room , whose door no. are 1,2,...n, initially all doors are closed. A person takes n round of the row, numbers as 1st round, 2nd round,....nth round. In each round he interchange the position of those door no. whose number is multiple of round no. Find out after nth round ,How many doors will be open.
The answer is √n
My approach let n be 4. Let C=Closed, O=Open
HENCE after 4 round we 2 open viz √4=2
This indicate that my apprach is corect but want to formulate it. Please help me