I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?

Can you solve this tricky maths equation problem by replacing it? mark with the correct symbol?

19834 -----: 187
15921 -----: 153
17561 -----: 139
13734 -----: ???

The following sentence is false. The preceding sentence is true.
Are these two sentences true or false?

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.

You have 21 jars with you. Out of them, 7 are filled with water, 7 are half-full with water and 7 are empty. How will you distribute the jars among three people such that each one of them gets an equal number of jars and an equal amount of water?

Buy me, smell me or deliver me, I do not change.

Who am I?

Can you find a pattern and the missing number in the series given below?

100, 155, 258,? , 584, 819.

A man was telling some of his war stories to his grandchildren.
"When the World War I was on the verge of end, I was awarded for my bravery for I had saved a group of my men." He coughed and then added, "When we were fighting in northern France, an enemy soldier threw a grenade at us. Before it could explode, I picked it up and threw it away. For my act of bravery, right before the war ended, A General gave me a sword engraved with the words "Awarded for Display of Bravery and Heroism in World War 1"."

Hearing this, one of the grandson spoke up. "Grandpa, this is not a true story. It can"t be true!"

The truth is that it was not. How did the grand children know it?

I am the beginning of the end, and the end of time and space. I am essential to creation, and I surround every place. What am I?

Using the clues below, what four numbers am I thinking of?

The sum of all the numbers is 31.
One number is odd.
The highest number minus the lowest number is 7.
If you subtract the middle two numbers, it equals two.
There are no duplicate numbers.