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?

Below is the sum of symbols in each row and column in the figure. Analyzing the figure, can you find out the value of the symbols?

What's the next in the series?

H, Be, F, S, Mn, Kr, In, Gd, Tl, ?

How far can you walk into the woods?

You are given a set of weighing scales and 12 marbles. The scales are of the old balance variety. That is, a small dish hangs from each end of a rod that is balanced in the middle. The device enables you to conclude either that the contents of the dishes weigh the same or that the dish that falls lower has heavier contents than the other. The 12 marbles appear to be identical. 11 of them are identical, and one is of a different weight. Your task is to identify the unusual marble and discard it. You are allowed to use the scales three times if you wish, but no more. Note that the unusual marble may be heavier or lighter than the others. You are asked to both identify it and determine whether it is heavy or light

In Greek mythology, the Sphinx sat outside of Thebes and asked this riddle of all travellers who passed by. If the traveller failed to solve the riddle, then the Sphinx killed him/her. And if the traveller answered the riddle correctly, then the Sphinx would destroy herself. The riddle:

What goes on four legs in the morning, on two legs at noon, and on three legs in the evening?

Oedipus solved the riddle, and the Sphinx destroyed herself.

In the given figure, move three matchsticks so that the resulting figure contains two rectangles.

A number can be multiplied by multiple of nine
i.e 9 18 27 36 45 ...

and the resulting number consist of only one digit.

Can you identify the number ?

Can you find a five letter word that is left with only two letters if one is removed?

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

18 X 12 X 2 X 3 = 111