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

Assume there are approximately 5,000,000,000 (5 billion) people on Earth. What would you estimate to be the result, if you multiply together the number of fingers on every person's left hand? (For the purposes of this exercise, thumbs count as fingers, for five fingers per hand.) If you cannot estimate the number then try to guess how long the number would be.

A man plots the murder of his wife. His plan is full proof. Nobody saw them leaving their house. He stabbed her with a knife while driving. She died on the spot. He threw her body in a valley. He threw the knife carefully wiping his finger prints on a random garbage bin. Then he went back to his home and no one was watching him this time as well.

After an hour, he was called by the local police department who informed him that his wife was murdered. They asked him to reach the scene of crime immediately. But as soon as he arrived at the crime scene, he was arrested by them.

How did the police know that he himself is the murderer?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

Evil warlock dislikes dwarfs and therefore he selects four of them and buries them. The dwarfs are buried in the ground and they are in such a way that except for their heads, their body is inside the ground. The dwarfs cannot move their body and they can view only forward. They are all buried in a line, and amongst the four, one of the dwarfs is separated by a wall. All the dwarfs are in the same direction. The last dwarfs can see two heads of friends in the front and a wall. In the last second dwarf can see one head of his friend and a wall. The second dwarf can see only the wall. The dwarf can see nothing.
Warlock comprehends the situation and tells the dwarfs that he has placed hats on their heads. There are two blue hats and two red ones. In all four dwarfs, one of them has to say what colour hat he is wearing. If the dwarf says the correct colour of the hat, they will be left free. If the answer is wrong, then they will be dug inside the ground till the very end.

What will be the answer by the dwarf and how will they answer?

The host of a game show offers the guest a choice of three doors. Behind one is an expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?

Luis Garavito killed Density x Volume.

Who is Luis Garavito ?

Count the Triangle in the figure given below:

Forwards I am heavy, backward I am not. What am I?

One day, all the courtiers from Akbar's court were gathered in the assembly hall when one of them told the Emperor that all his valuables had been stolen by a thief the previous night.
This shocked the Emperor to his core as the place where that courter stayed was the most secured in the kingdom. The Emperor thought that it is not at all possible for an outsider to enter into the courtier's house and steal the valuables. Only another courtier could commit this crime. He quickly called Birbal to identify the thief.
Birbal thought for a while and successfully solved the mystery by identifying the thief in just one statement.
What did Birbal say?