Can you find a number that lies one third of the distance between 1/3 and 2/3?

I never was there, I am always to be.
You have never ever seen me, not ever you will.
Yet I am the confidence of everyone.

Who 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?

There are three identical triplets sisters. Demi is the oldest of them all and she always speaks the truth. Diana is the next one who is a liar always. Drew, the youngest of them all speaks both truth and lies randomly.

On a rainy day, a family friend Victor visited them. Since there were starkly identical, he was not able to recognize them. Thus to clarify, he asked one question to each one of them.

He started with the one standing on the left and asked, 'Which sister is in the middle of you three?' She answered, 'That's Demi.'

Then, he asked the one standing in the middle, 'What is your name?' She answered, 'I am Drew.'

Finally, he asked the one standing on the right, 'Who is standing in the middle?' She answered, 'She is Diana.'

Victor was left baffled. He asked the questions three times and received different answers every time.

Can you tell who was who?

An equation has been laid down using a few matchsticks. However, as you can see, the equation is not correct. Can you correct the equation if you are allowed to add or remove 5 matchsticks?

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

What is both possible and impossible at the same time?

What does below science rebus mean?

Ag Ag Ag
Ag SPOON Ag
Ag Ag Ag

When I asked a girl's name she told me her name is the date '07/09/2001'.

I thought for a few seconds and then I got her name. Do you?

The owner of a popular clothing store comes up with his own method of pricing items. A vest costs $8, socks cost $10, a tie costs $6, and a blouse costs $12. Using the owner’s method, how much would a pair of underwear cost?