Can you find a number that lies one third of the distance between 1/3 and 2/3?

I am a white box having no key or lid.
Yet there is a golden treasure inside it.

What Am I?

10 people came into a hotel with 9 rooms and each guest wanted his own room. The bellboy solved this problem.
He asked the tenth guest to wait for a little with the first guest in room number 1. So in the first room, there were two people. The bellboy took the third guest to room number 2, the fourth to number 3, ..., and the ninth guest to room number 8. Then he returned to room number 1 and took the tenth guest to room number 9, still vacant.
How can everybody have his own room?

John was piloting a plane behind a car but was never able to overtake it. Why?

The more you take me, the more you leave me behind.
Who Am I?

Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

In a town, there are four houses located at different distances from each other. Following are the distances:

The third house is 60 meters apart from the first house.
The fourth house is 40 meters apart from the second house.
The third house is 10 meters nearer to the fourth house than it is to the second house.

Can you find out the distance between the fourth and the first house?

what's the probability of getting a king or a queen from a pack of 52 cards?

Who are the happiest people in IPL match?

There are three boxes. One is labeled "APPLES" another is labeled "ORANGES". The last one is labeled "APPLES AND ORANGES". You know that each is labeled incorrectly. You may ask me to pick one fruit from one box which you choose.

How can you label the boxes correctly?