Replace the question mark with the number below given a simple math problem.

How can a man go eight days without sleep?

A sea diver is a real show-off. He showed everyone that he can hold his breath underwater for 15 minutes.

I went to the diver and told him that I can be underwater for double the time i.e 30 minutes.
He responded that he will give me 100$ if I would be able to do it. I won 100$.

What did I do?

You have four chains. Each chain has three links in it. Although it is difficult to cut the links, you wish to make a single loop with all 12 links. What is the fewest number of cuts you must make to accomplish this task?

If we tie a Sheep to one peg, a circled grass is been eaten by the Sheep. If we tie the Sheep to two pegs with a circle on its neck, then an eclipse is eaten out of the grass by the Sheep. If we want an eclipse then we put two pegs and then put a rope in between them and the other end of the rope is tied up on the Sheep's neck.

How should we tie the peg and the Sheep so that a square is eaten out from the garden grass? We only have one Sheep rope and the peg and the rings.

The following alphametic has only one solution. Can you find it?
ENLIST + SILENT + LISTEN = ANAGRAM

PS: You may start the number from 0.

What is the four-digit number in which the first digit is one-third the second, the third is the sum of the first two, and the last is three times the second?

What can run but never walk, have a mouth that never speaks, have a head that never weeps, and have a bed but never sleeps?

An artist while painting a scenic beauty, decides to paint three layers of blue colour on the sky.

Which layer will go on the first?

There are two dice with empty faces in front of you and a marker. You can mark any number on each of the faces of the two dice, but you have to display all 31 days of the month using the two of them.

Which numbers will you mark on which dice so that you can easily depict all the dates of the month?