What's the only room from which no one can enter or leave

Can you replace the question mark with the correct letter?

6 + 6 + 6 = N
7 + 7 + 7 = E
8 + 8 + 8 = R
0 + 0 + 0 = ?

It's a 7-letter word.
If we remove 1 letter from it, it remains the same.
If we remove 2 letters from it, it remains the same.
If we remove 3 letters from it, it remains the same.
If we remove all the letters from it, still it remains the same.
What is it?

A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?

If there are fifteen crows on a fence and the farmer shoots a third of them, how many crows are left?

There are five vowels (a, e, i, o, u) in the English language.
Can you tell us a word that contains all these vowels?

Why do people go to bed?

Why is the Hole below a Lock?

Take away my first letter, then take away my second letter. Then take away the rest of my letters, yet I remain the same. What am I?

I have branches, but no fruit, trunk or leaves. What am I?