There are 1000 doors that are of the open-close type. When a person opens the door he closes it and then opens the other. When the first person goes he opens-closes the doors in the multiples of 1 i.e., he opens and closes all the doors. when the second goes he opens and closes the doors 2, 4 6 8 respectively. Similarly when the third one goes he does this for 3 6 9 12 15th doors respectively. Find number of doors that are open at last.\nOptions:\n(A) 29\n(B) 31\n(C) 32\n(D) 24\n(E) 21 OK. Let's think. Some random thoughts first:
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31. only the perfect squares between 1 to 1k The answer: (B).
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