why number 8549176320 is one of a kind?

I live in a bowl. I can swim. I have a tail. I also have fins and big eyes. What am I?

I look at you, you look at me I raise my right, you raise your left. What am I?

If I put in one bird per cage, I have one bird too many. If I put in two bird per cage, I have one cage too many. How many cages and birds do I have?

How is the moon similar to a dollar?

You are given four results as below:
1111 = F
2222 = E
3333 = T
Then, can you find out how to code 4444?

When we see 2 but call 10?

There are 20 people in an empty, square room. Each person has full sight of the entire room and everyone in it without turning his head or body, or moving in any way (other than the eyes). Where can you place an apple so that all but one person can see it?

You are given 16 witch hats. The hats are divided in four different colours – red, blue, green and yellow. Every colour has been assigned to four hats. Now each of the hat will be glued with a label of an arithmetic sign – ‘+’, ‘-‘, ‘x’ or ‘/’. But you can label one sign only once on one colour. In such an arrangement, the hats can be uniquely defined by its colour and symbol.

Can you arrange all the 16 hats in a 4x4 grid in a fashion that no two rows and columns have a repetition of colour or sign?
We have arranged four hats in the below picture to assist you.

Which is the smallest number that you can write using all the vowels exactly once?