Why do people go to bed?

A rubber ball keeps on bouncing back to 2/3 of the height from which it is dropped. Can you calculate the fraction of its original height that the ball will bounce after it is dropped and it has bounced four times without any hindrance ?

John enters a small room. The Door Closes.
When the door opens, John is in a larger room.

Explain?

A word I know,
Six letters contain,
Subtract just one,
And twelve is what remains.

What does Alexander the Great and Winnie the Pooh have in common?

A number can be multiplied by multiple of nine
i.e 9 18 27 36 45 ...

and the resulting number consist of only one digit.

Can you identify the number ?

One absent-minded ancient philosopher forgot to wind up his only clock in the house. He had no radio, TV, telephone, internet, or any other means for telling time. So he travelled on foot to his friend's place a few miles down the straight desert road. He stayed at his friend's house for the night and when he came back home, he knew how to set his clock. How did he know?

I have a five and a three-gallon jar. Assuming there is an infinite supply of water, how can I measure one-gallon water?

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?

A mathematician couple was having a Frappuccino in Starbucks sitting opposite to each other. Suddenly the guy noticed the text written on the paper in front of them and exclaimed that it was wrong. The girl denied it and said it is appropriate. Both are correct. What is written on the paper?