I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?

Using eight eights and addition only, can you make 1000?

A boy was at a carnival and went to a booth where a man said to the boy, "If I write your exact weight on this piece of paper then you have to give me $50, but if I cannot, I will pay you $50." The boy looked around and saw no scale so he agrees, thinking no matter what the carny writes he'll just say he weighs more or less. In the end the boy ended up paying the man $50. How did the man win the bet?

I was speeding and ran through a stop sign, yet two traffic officers who were there do nothing about it.

why?

I have a mouth but I don't eat.
I have a bank but have no money.
I have a bed but i dont sleep.
I wave but have no hands.

Who Am I ?

The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member ?

A boy was locked in a room by some robbers. All that is in the room is a piano, a calendar, and a bed. The room is locked from the outside. What does he eat, drink, and how does he escape and get out?

Can you count the number of squares in the figure below?

A man was gazing through the window of the 23rd floor of the building. He suddenly opened the window and jumped on the other side of the window. On landing on the floor, there was not a sheer mark of injury on him.

How can that be possible if he did not use any kind of parachute and did not land on a soft surface?