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?

What goes through cities and fields, but never moves?

As easy as you can get into me, it is as hard to get out of me.

Do you know what I am?

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

The ages of a father and son add up to 66.
The father's age is the son's age reversed.
How old could they be?
(3 possible solutions).

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

What work can one never finish?

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

There is something which you can be arrested for attempting but not for successfully completing.

There's one "sport" in which neither the spectators nor the participants know the score or the leader until the contest ends.

What is it?