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?

If we tell you that there is a relation between the numbers and letters in the given figure, can you analyze it and find the missing letter in the last box?

You are given a cube that is made with the help of 10x10x10 smaller cubes summing up to a total of 1000 smaller cubes. You are asked to take off one layer of the cubes.
How many remain now?

What month of the year has 28 days?

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?

How can you drop a raw egg from a height onto a concrete floor without cracking it?

Two girls were born to the same mother, on the same day, at the same time, in the same month and year and yet they're not twins. How can this be ?

Four men were in a boat on the lake. The boat turns over, and all four men sink to the bottom of the lake, yet not a single man got wet! Why?

What has a ring but no finger?

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?