How can a man go eight days without sleep?

I am lying and I always lie. Tell me whether I am lying or telling the truth.

They are three errirs in this question. Can you find them?

There is a shop where written:
Buy 1 for $1
10 for $2
100 for $3
I needed 999 and still only paid $3. How could this be financially viable for the shop-keeper?

Rectify the following equality 101 - 102 = 1 by moving just one digit.

I am a number I am not an odd number I am higher than 90 I am not higher than 100 If you subtract me from 100, you get nothing. What number am I?

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?

10+10 and 11+11 can give you the same answer.

Explain how?

If 1+9+8=1, what is 2+8+9?

Can you find out what is missing?

1 3 5
2 4 ?

Hint: It's not six. Think out of the box.