Create a number using only the digits 4,4,3,3,2,2,1 and 1. So i can only be eight digits. You have to make sure the ones are separated by one digit, the twos are separated by two digits the threes are separated with three digits and the fours are separated by four digits

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?

It's pretty hard to give up.
If you remove a part of it, you will be left with a bit.
Even if you remove another part, the bit still remains.
Remove one more and it still remains.

What is it?

With the following rules:

(A) White can make up to 10 legitimate moves until all kings are checkmate.
(B) White can take any black piece except the king.
(C) The White King cannot be in check position at any time of the game.

Can you checkmate all kings in less than 10 moves?

What demands an answer, but asks no questions

P is the father of Q and S is the son of R. T is the brother of P and has a daughter U. If R is the sister of P, then what is the relation between U, Q and S?

Jessica is telling her friends this story and asks them to guess if it’s the truth or a lie: “There was a man sitting in a house at night that had no lights on at all. There was no lamp, no candle, and no other source of light. Yet, he sat in the house and read his book happily.” Her friends say she’s lying, but Jessica corrects them and says she’s telling the truth. Jessica’s story is true—but how?

What came first, the chicken or the egg?

We are a group of eight brothers. We consider the weak, yet we protect the king in every battle. If we move ahead, we never turn back. Who are we?

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?