# 1000 Doors

Number Theory Level pending

In a room there is $$1000$$ doors and each door is numbered $$1$$ to $$1000$$. Initially all the doors are closed. In a group of 1000 people each one of them is also numbered $$1$$ to $$1000$$. Person with numbered 1 goes inside the room and opened all the doors, person with numbered 2 then goes next and closed all the doors which are multiple of two. In general, $$r^{th}$$ person changes the state of those doors having multiple of r. All the $$1000$$ person does the same. After this practice how many doors will be remain opened $$?$$

NOTE : A person doesn't touch other doors which are not multiple of his number

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