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

A farmer and his neighbour once went to Emperor Akbar"s court with a complaint. "Your Majesty, I bought a well from him," said the farmer pointing to his neighbour, "and now he wants me to pay for the water."
"That"s right, your Majesty," said the neighbour. "I sold him the well but not the water!"?
The Emperor asked Birbal to settle the dispute. How did Birbal solve the dispute?

Luis Garavito killed Density x Volume.

Who is Luis Garavito ?

There's one "sport" in which neither the spectators nor the participants know the score or the leader until the contest ends.

What is it?

For this puzzle, you might have to find logic in something illogical. But hey, it's fun and a healthy little break from your strenuous puzzle-solving sessions.

Can you decipher the meaning in the following cluster of letters?

ITIT,NCENTCENT

How can a man go eight days without sleep?

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

What breaks yet never falls, and what falls yet never breaks?

Which is faster, Heat or Cold ? Explain.

An apple seller is hosting a competition. He offers 1000 apples and 10 boxes to the people who pass by. The challenge is to put those 1000 apples in the 10 boxes in such a manner that if he asks for any amount of apples, the person can directly give him the boxes or a combination of boxes. If the person can do it, he promises to give a thousand apples for free.

If you happen to pass by the apple seller, will you be able to win a thousand apples?