If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

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

Your last good ping-pong ball fell into a narrow metal pipe embedded one foot deep in concrete.
How can you get it out undamaged, if all the tools you have are your tennis paddle, shoe laces, and plastic water bottle, which does not fit into the pipe?

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

The captain of a ship was telling this interesting story: "We travelled the sea far and wide. At one time, two of my sailors were standing on opposite sides of the ship. One was looking west and the other one east. And at the same time, they could see each other clearly." How can that be possible?

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

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?

What word begins and ends with an E, but has only one letter?

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?

You are playing a game with your friend Jack. There are digits from 1 to 9. You both will take turn erasing one digit and adding it to your score. The first one to score 15 points will win the game.

Would you want to play first or second?

PS: The sum should be exactly 15.