A word I know has six letters it contains, remove one letter and 12 remain. What is it?

A man is shown a portrait painting. He looks closely, then tells, “Brothers and sisters have I none, but that man’s father is my father’s son!” Who is the man in the portrait?

John said, "If yesterday was tomorrow, today would be Friday."

When did John make this statement?

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

Find the next number in the series

12, 20, 40, 72, 116, 172 ?

There is a box full of marbles,
all but two are blue,
all but two are green,
and all but two are red.

How many marbles are in the box?

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

Can you identify the hidden rebus in the image below?

Two old friends, Jack and Bill, meet after a long time.

Three kids
Jack: Hey, how are you, man?
Bill: Not bad, got married and I have three kids now.
Jack: That's awesome. How old are they?
Bill: The product of their ages is 72 and the sum of their ages is the same as your birth date.
Jack: Cool..But I still don't know.
Bill: My eldest kid just started taking piano lessons.
Jack: Oh, now I get it.

How old are Bill's kids?

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?