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?

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

How can you tell a raw egg from a hard-boiled egg?

I am a seven-letter word but if you remove four of my letters I will have one left. What word am I?

The centre of the third figure is empty. What digit should fit inside?

Can you move 2 matchsticks to form four equal sized squares.

Replace the question mark in the picture below.

In the attached figure, you can see a chessboard and two rooks placed on the chess board. What you have to find is the number of squares that do not contain the rooks. How many are there?

There’s a one-story house in which everything is yellow. Yellow walls, yellow doors, yellow furniture. What colour are the stairs?

Can you find the least possible number such that

If the number is divided by 3, it gives the remainder of 1;
If the number is divided by 4, it gives the remainder of 2;
If the number is divided by 5, it gives the remainder of 3;
If the number is divided by 6, it gives the remainder of 4.