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

The answer is 31.

**
This section requires Javascript.
**

You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.

No explanations have been posted yet. Check back later!