What is both possible and impossible at the same time?

On a magical land of Mexico , all the animal in the land are rational.

There are 10 tigers and one goat.
Tiger can eat goat but since it's a magical land , the tiger who eats the goat , turns into goat and then can be eaten by the remaining tiger(s).

If we leave them for some time then how many goat and tiger will be there , when we come back ?

What came first, the chicken or the egg?

Today, I celebrated my 32nd birthday but I was born in 1972.
How is this possible?

There is a unique number which when multiplied by any number from 1 to 6, we will get the new number that contains the same digits only.

Can you find that number?

I am a normal creature, but I have five hands. I can even have more but even then I will be considered normal.

Who am I?

Can you name three consecutive days without using the words Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, or Sunday?

A man walked into a pub and went straight towards the Barman. He asked for a dirty martini from the Barman. The Barman thought something and then pulled out a pistol from his drawer and aimed it directly at the man. Why did he do that?

I am five letter word that is under you.
If you remove my 1st letter, then I am over you.
If you remove my 1st and 2nd letters then I am all around you.

Who am I?

In Greek mythology, the Sphinx sat outside of Thebes and asked this riddle of all travellers who passed by. If the traveller failed to solve the riddle, then the Sphinx killed him/her. And if the traveller answered the riddle correctly, then the Sphinx would destroy herself. The riddle:

What goes on four legs in the morning, on two legs at noon, and on three legs in the evening?

Oedipus solved the riddle, and the Sphinx destroyed herself.