A father's child, a mother's child, yet no one's son.

Who am I?

You have a 12 liters jug full of water. You have two empty 8 liters and 5 liters jug. How can you divide the water into two equal parts using these jugs?

What has no start, end, or centre?

Replace the 'X' with any mathematical symbol to make the expression equal to 111.

18 X 12 X 2 X 3 = 111

There is a circular car race track of 10km. There are two cars, Car A and Car B. And they are at the exact opposite end to each other. At Time T(0), Both cars move toward each other at a constant speed of 100 m/seconds. As we know both cars are at the same speed they will always be the exact opposite to each other.
Note, at the center, there is a bug which starts flying towards Car A at time T(0). When the bug reaches car B, it turns back and starts moving towards the car A. The speed of bug is 1m/second. After 5 hours all three stop moving.
What is the total distance covered by the bug?

How many letters are in the alphabet?

Replace the (?) with the correct mathematical signs to make the expression equal to 59.

18 ? 12 ? 4 ? 5 = 59

A man escapes from jail using help from his girlfriend. The investigators suspect four girls of being the man's girlfriend.

Out of those four girls, one is his girlfriend who is lying. Two of the girls are completely innocent and are speaking the truth. One of the girls is the man's sister who is helping the girlfriend lie. Following are the statements from all four of them:

Ariana: "Myrna is his girlfriend."
Jane: "Angelina is lying."
Angelina: "Ariana is lying."
Myrna: "Jane is not his sister."

Can you find out who is the man's sister among them?

Can you solve below mathematical equation?

2^1234 - 2^1233

A woman lives in a Tall building thirty-six floors high and served by several elevators which stop at each floor going up and down. Each morning she leaves her apartment and goes to one of the elevators. Whichever one she takes is three times more likely to be going up than down. Why?