Our product and our sum always give the same answer. Who are we?

In one of the popular batman series movie "Batman Forever", there was a riddle that goes like "Tear me off and then scratch my head and I was red then and now I am back. Who am I?

What is the coolest letter in the alphabet?

81 x 9 = 801. What must you do to make the this equation true?

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?

Can you count the number of lines in the below picture?

Where do fish keep their money?

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

Nodes are shown below and you need to connect them based on the following rule: Every node can be connected to the number of nodes inside them, i.e. the first node there is a value of 1 which indicates that the first node can connect to exactly one node only.Can you do it?

A plane crashed between the border of Mexico and America. Where do you bury the survivors?