What is wrong in the below Picture?

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 am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

A man says, "Brothers and sisters, have I none, but that man's father is my father's son." Who is that man?

Can you solve this amazing hard number series problem?
7, 8, 10, 12, 16, 18 ?

John's five friends Rachel, Jacob, Phoebe, Joey and Chandler live on the same road.

Rachel lives in the house: A, Jacob lives in the house: B, Phoebe lives in the house: C, Joey lives in the house:D, Chandler lives in the house: E

Mathematically
B*C*D = 1260
B + C + D = 2E
2A = E

The road numbers run from 2 to 222.

Can you tell me the house number of each of John's friends?

Is the statement valid that it does not matter how much older a sibling is, eventually the younger one will be half as old as the older one?

There are two words one resembles the "state of rest" and the other is related to "writing/reading material".

Can you name these two words which also sound similar?

You need to arrange three 7 and mathematical symbols to form number 1?

I ask Joseph to pick any 5 cards out of a deck with no Jokers.

He can inspect then shuffle the deck before picking any five cards. He picks out 5 cards then hands them to me (Jack can't see any of this). I look at the cards and I pick 1 card out and give it back to Joseph. I then arrange the other four cards in a special way, and give those 4 cards all face down, and in a neat pile, to Jack.

Jack looks at the 4 cards i gave him, and says out loud which card Joseph is holding (suit and number). How?

The solution uses pure logic, not sleight of hand. All Jack needs to know is the order of the cards and what is on their face, nothing more.