What always comes into a house through the keyhole?

There is a square of a particular number which when doubled, becomes 7 more than its quarter.

Can you find the number?

You are trapped into a death trap by the famous jigsaw killer. As usual, a screen flashes in front of you and explains you the trap game. There are 100 pearls kept in a bowl in front of you and an empty bowl. Among the 100 pearls, 50 are white and 50 are black. You can divide them as you like into the two bowls. Once you are done, you will pull a lever, which will turn the room pitch black. The bowls will move and shuffle around. In the dark, you have to pick up one pearl from any bowl. Once you do that, the room will flood with lights again. If the peral you have in your hand is white, you will be allowed to live, but if the pearl you picked is black, the room will be filled with poisonous gas and you will die. How will divide the pearls to increase your chances of survival?

The barber of Town shaves all men living in the town. No man living in the town is allowed to shave himself. The barber lives in that town. Who then shaves the barber of the town?

I have a five and a three-gallon jar. Assuming there is an infinite supply of water, how can I measure one-gallon water?

There are nine dots in the picture that has been attached with this question. Can you join all the dots by drawing four straight lines without picking up your pen?

Identify Me

Hint1: I am a god
Hint 2: I am a planet
Hint 3: measurer of heat

A time long back, there lived a king who ruled the great kingdom of Trojan House. As a part of the renovation of the kingdom to meet future security needs, he asked his chief architect to lay down a new play in a manner that all of his 10 castles are connected through five straight walls and each wall must connect four castles together. He also asked the architect that at least one of his castles should be protected with walls. The architect could not come up with any solution that served all of King's choices, but he suggested the best plan that you can see in the picture below. Can you find a better solution to serve the king's demand?

If a boy blows 18 bubbles,
Then pops 6 eats 7 and then
He pops 5 and blows 1.
How many are left?

I was born in a small house and I live in it all alone. No windows and no doors have been assigned to my house. The only way I can go out is by breaking through the walls of my house.

Who am I?