I have an eye but still cannot see.

Who am I?

A woman lives in a Tall building thirty-six floors high and served by several elevators which stop at each floor going up and down. Each morning she leaves her apartment and goes to one of the elevators. Whichever one she takes is three times more likely to be going up than down. Why?

You can win me and lose me but never buy me
You can not eat me and never want to part with me
I can make you cry or bring you joy
I am not a machine and definitely not a toy
You keep me but i am not forever just yours
You might find me in a case or on a shelf next to a vase
I am hard and i am tall if you bump me i am sure to fall
I am made of different materials and am at many events
If your lucky and fight hard I might be yours
What am I ?

There is an English word that can be used up to four times in a row without modifying the spelling and form a valid grammatical sentence.

Do you know what word is that?

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?

You are stuck on an island where you have nothing. You find four pieces of paper somewhere on the island. What will be your strategy to escape from the island safely?

PS: No other resource is available to you on the island, neither can you build anything.

What is a word made up of 4 letters, yet is also made up of 3. Sometimes is written with 9 letters, and then with 4. Rarely consists of 6, and never is written with 5.

What does man love more than life, hate more than death or mortal strife; That which contented men desire; the poor have, the rich require; the miser spends, the spendthrift saves, and all men carry to their graves?

If a wheel has 54 spokes, how many spaces are there between the spokes?

Can you find a number that lies one third of the distance between 1/3 and 2/3?