Prove that twice of ten is the same as twice of eleven.

You are an expert on paranormal activity and have been hired to locate a spirit haunting an old resort hotel. Strong signs indicate that the spirit lies behind one of four doors. The inscriptions on each door read as follows:

Door A: It's behind B or C
Door B: Its behind A or D
Door C: It's in here
Door D: It's not in here

Your psychic powers have told you three of the inscriptions are false, and one is true. Behind which door will you find the spirit?

I am taken from a mine and shut up in a wooden case, from which I am never released, and yet I am used by almost every person. What am I?

If EELS + MARK + BEST + WARY = EASY

What does HELP + BARK + WARD + LEAD equal?

The person who makes it has no need for it; the person who buys it has no use for it. The person who uses it can neither see nor feel it. What is it?

Can you find the missing piece of the Porsche?

The barber of Town shaves all men living in the town. No man living in the town is allowed to shave himself. The barber lives in that town. Who then shaves the barber of the town?

I am the one who remains awake when you sleep. But I need to rest when you awake. Who Am I?

I have a hole in my back and legs I lack.
I live where I can’t breathe and I eat without teeth.
What am I?

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