What is both possible and impossible at the same time?

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 ?

For this puzzle, you might have to find logic in something illogical. But hey, it's fun and a healthy little break from your strenuous puzzle-solving sessions.

Can you decipher the meaning in the following cluster of letters?

ITIT,NCENTCENT

Two friends were betting. One said to the other, "The coin will be flipped twenty times and each time the coin lands on the head, I will give you $2 and each time it lands on the tale, you will give me $3." After flipping the coin twenty times not a single penny was exchanged among them.

How many times did the coin land on heads?

You knock a Table over in the library, and suddenly 20 eyes are looking at you.

What am I?

I am lying and I always lie. Tell me whether I am lying or telling the truth.

Can you find out a way through which you can make five squares out of the given figure by moving just six match sticks?

A car meter reading shows 72927 miles a palindromic number.
what is the minimum number of miles you would need to travel to see another palindromic number on the car meter reading?

A doctor and a boy were fishing. The boy was the doctor’s son, but the doctor was not the boy’s father. Who was the doctor?