How can a man go eight days without sleep?

We have shown you a regular water barrel as below. Without using any measuring device can you check if the barrel is more than half-filled or less than half-filled?

Can you count the number of triangles in the given figure?

There is a basket full of hats. Three are white and two are black. Three men, Tom, Tim, and Jim, each take a hat out of the basket and put it on their heads without seeing the hat they selected or the hats the other men selected. The men arrange themselves so Tom can see Tim and Jim’s hats, Tim can see Jim’s hat, and Jim can’t see anyone’s hat. Tom is asked what color his hat is and he says he doesn’t know. Tim is asked the same question, and he also doesn’t know. Finally, Jim is asked the question, and he does know. What colour is his hat?

A man has eighty-one cows ( numbered 1,2,3...81 as such). The beauty is that cow no. 1 gives 1ltr of milk, cow no. 2 gives 2ltrs of milk and so on. The man wants to equally distribute the cows among his nine sons so that each one of them gets the same quantity of milk.

What is both possible and impossible at the same time?

My friends called me Iron59 because my parents are a chemist and a mathematician. What is my real name?

I can sizzle like bacon,
I am made with an egg,
I have plenty of backbone, but lack a good leg,
I peel layers like onions, but still remain whole,
I can be long, like a flagpole, yet fit in a hole.

What has no start, end, or centre?

What number comes next in this sequence:
7 8 5 5 3 4 4 _