I am the one who remains awake when you sleep. But I need to rest when you awake. Who Am I?

Replace the letters of words with a number so that the below equation holds true

BASE +
BALL
---------
GAMES
----------

Make the seating arrangement of 10 children in such a way that there are 5 rows with 4 children in each row.

Can you count the number of lines in the below picture?

Once upon a time, there was a castle on a square island. The entire island was surrounded by a 14m wide trench. The Romans had wanted to invade the castle and had brought a few wooden planks along with them to facilitate themselves in crossing the moat. The planks were however found to be only 13m long.

The Romans still managed to cross the trench. How did they do it?

You have two jars of chocolates labelled as P and Q. If you move one chocolate from P to Q, the number of chocolates on B will become twice the number of chocolates in A. If you move one chocolate from Q to P, the number of chocolates in both the jars will become equal.

Can you find out how many chocolates are there in P and Q respectively?

Can you find out the remainder when 3^300 is divided by 5?

If you were to put a coin into an empty bottle and then insert a cork into the neck, how could you remove the coin without taking out the cork or breaking the bottle?

Christina has four daughters, and each of her daughters has a brother. How many children does Christina have?

There are five people. One of them shot and killed one of the other five.
We know following clues:
1. Dan ran in the NY City Marathon yesterday with one of the innocent men.
2. Mike consider being a farmer before he moved to the city.
3. Jeff is a top notch computer consultant and wants to install Ben new computer next week.
4. The murderer had his leg amputated last month.
5. Ben met Jack for the first time six months ago.
6. Jack has been in seclusion since the crime.
7. Dan used to drink heavily.
8. Ben and Jeff built their last computers together.
9. The murderer is Jack's brother. They grew up together in Seattle.

Consider yourself to be a famous detective "Sherlock Homles", Can you find the killer?