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?

2, 3, 5, 9, 17, _ What is the next number in the sequence?

If you’ve got me, you want to share me; if you share me, you haven’t kept me. What am I?

By moving just one matchstick, you need to make the below statement true. Can you do it?

When you stop to look, you can always see me. But if you try to touch me, you can never feel me. Although you walk towards me, I remain the same distance from you. What am I?

John is selling fruits.
He sells grapes at $30, Dates $25, and a Wolfberry $45.
At what price does he sell fig?

PS: Logical Thinking

I sleep during the day and fly at night, but I have no feathers to aid my flight. What am I?

You may enter, but you may not come in. I have space, but no room. I have keys, but open no lock. What am I?

I add 5 to 9 and get 2. The answer is correct, so what am I?

In a mathematical quiz, you are asked the following question:

Use three 9s in a mathematical expression without dividing or multiplying to form the number one.

Can you answer the question?