What has to be broken before you can use it?

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?

The below mentioned letters have been placed in a order using a logic.

DEAD, BALL, FEAR, SHOP

Can you find the logic?

Can you think of a smallest +ve number such that if we shuffle the digits of the number, the new number becomes double the original number?

What number should come in place of the question mark below?

The ages of a father and son add up to 66.
The father's age is the son's age reversed.
How old could they be?
(3 possible solutions).

The more of this there is, the less you see. What is it?

A cat, a dog and a monkey were stolen. 3 suspects got caught: Harish, Manoj and Tarun. All we know is each person stole one animal, but we do not know who stole which. Here are the investigation statements. Harish said: Tarun stole the cat. Manoj said: Tarun stole the dog. Tarun said: They both were lying. I did not steal the cat or the dog. Later on, the police found out the man who stole the monkey told a lie. The man who stole the cat told the truth. Can you find out who stole which?

There’s a girl who has a large family. She has an equal amount of brothers and sisters, but each brother only has half as many brothers and sisters. What’s the correct amount of brothers and sisters?

A journalist was investigating a sacred cult in the jungles of Africa when he was caught by one of the person. He was confined in a cave till the leader arrived. The leader told him that he need to tell him a statement. If he thinks the statement is true, then the journalist head will be chopped off. If he thinks that the statement is false, his head will be smashed with a hammer.

What statement did the journalist make to survive?