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

I am soft and cuddly that soothe your heart. But, If you pick my last name I am going to tear you all apart. Who am I?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

I have branches, but no fruit, trunk or leaves. What am I?

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

What is at the end of a rainbow?

If you remove one from eleven, it becomes ten. If you remove one from nine, it becomes ten.

How is this possible?

You may enter, but you may not come in. I have space, but no room. I have keys, but open no lock. What am I?

Three people enter a room and have a green or blue hat placed on their heads. They cannot see their own hat but can see the other hats.
The colour of each hat is purely random. They could all be green, blue, or any combination of green and blue.
They need to guess their own hat colour by writing it on a piece of paper, or they can write 'pass'.
They cannot communicate with each other in any way once the game starts. But they can have a strategy meeting before the game.
If at least one of them guesses correctly they win $10,000 each, but if anyone guesses incorrectly they all get nothing.
What is the best strategy?

If you had a pizza with crust thickness 'a' and radius 'z', what's the volume of the pizza?