People put me on the table and cut me but do not eat me. What am I?

When you say goodbye, I am what you need to tie.
I come as a couple and go wherever you run.
Who 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?

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

What can run but never walk, have a mouth that never speaks, have a head that never weeps, and have a bed but never sleeps?

The dirtier I get, the whiter I look. Who am I?

A tree doubled in height each year until it reached its maximum height over the course of ten years. How many years did it take for the tree to reach half its maximum height?

Rob is taller than Edwin, and Jurgen is shorter than Rob.
Of only one of the following statements, we now certainly know it is correct:

A.Edwin is taller than Jurgen
B.Jurgen is taller than Edwin
C.It cannot be determined if Jurgen or Edwin is the tallest.

Can you divide the below-given shape into four equal and identical pieces?

10 people came into a hotel with 9 rooms and each guest wanted his own room. The bellboy solved this problem.
He asked the tenth guest to wait for a little with the first guest in room number 1. So in the first room, there were two people. The bellboy took the third guest to room number 2, the fourth to number 3, ..., and the ninth guest to room number 8. Then he returned to room number 1 and took the tenth guest to room number 9, still vacant.
How can everybody have his own room?