# 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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