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?

Name a key which is hardest to turn.

There is an English word that can be used up to four times in a row without modifying the spelling and form a valid grammatical sentence.

Do you know what word is that?

I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?

what does this below rebus represent identXQQQQQME

In a guessing game, five friends had to guess the exact numbers of apples in a covered basket.
Friends guessed 22, 24, 29, 33, and 38, but none of the guesses was correct. The guesses were off by 1, 8, 6, 3, and 8 (in random order).

Can you determine the number of apples in a basket from this information?

Which number should replace the question mark?

There is a brick of gold and a brick of iron in a boat (both 10-inch blocks), if they are both dropped into the water which will make the water level higher?

I am the largest in my family of fifty.
The youngest of our family lives separately from the rest of the family and so do I.
I am regarded as harsh and tough.
I am so large, you cut me in two equal halves,
each half would still be larger than the second largest member of the family.
Who am I?

Solve the following series:
AZ, GT, MN, __, YB