I travel all around the world but always stay in the corner. What am I?

I have lakes with no water, mountains with no stone and cities with no buildings. What am I?

The person who makes it has no need for it; the person who buys it has no use for it. The person who uses it can neither see nor feel it. What is it?

Only one colour, but not one size,
Stuck at the bottom, yet easily flies.
Present in sun, but not in rain,
Doing no harm, and feeling no pain.
What is it?

When Jack was six years old he hammered a nail into his favourite tree to mark his height. Ten years later at age sixteen, Jack returned to see how much higher the nail was. If the tree grew by five centimetres each year, how much higher would the nail be?

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?

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

I am a three digit number.
My tens digit is five more than my ones digit.
My hundreds digit is eight less than my tens digit.
What number am I?

I never stop running even when I standstill. If I am formed by joining two identical bodies together, can you guess who I am?

You order chicken wings at KFC in the boxes of 6, 9 and 20. What is the largest number of wings that you cannot obtain by buying in any combination of the boxes?