The more of this there is, the less you see. What is it?

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 can go up a chimney down, but can’t go down a chimney up?

There are two dice with empty faces in front of you and a marker. You can mark any number on each of the faces of the two dice, but you have to display all 31 days of the month using the two of them.

Which numbers will you mark on which dice so that you can easily depict all the dates of the month?

I taste better than I can smell. Who am I?

Use only one mathematical symbol and all numbers (0-9) to get a sum of 99

A man looks at a painting in a museum and says, “Brothers and sisters I have none, but that man’s father is my father’s son.” Who is in the painting?

If in a car race, the man who came two places in front of the last man finished one ahead of the man who came fifth, how many contestants were there?

If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

Below the four parts have been reorganised. The four partitions are exactly the same in both arrangements. Why is there a hole?