What is both possible and impossible at the same time?

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

A red house is made out of red bricks. A yellow house is made out of yellow bricks. And, a blue house is made out of blue bricks. So, what is a greenhouse made of?

Replace the question mark with the correct number.

John and Jacob are twin brothers. One of them is a liar whereas the other one is a truth-teller.

I called their home number and one of them picked up.
I asked. 'Does John lie?' The person replied with a yes.

Whom did I talk with, John or Jacob?

Below, you can see three complete equations and one incomplete. Based on the three complete ones, can you complete the incomplete one?

5 $ 4 $ 3 $ 9 = 4215
6 $ 9 $ 2 $ 6 = 3816
4 $ 7 $ 3 $ 3 = 1122
7 $ 2 $ 7 $ 4 = ____

If Bihan is 10, Anirudha is 20, and Kim and Seal are both 5, but Rikold is 10, how much is Kenniger by the same trend?

What has 88 keys?

When you stop to look, you can always see me. But if you try to touch me, you can never feel me. Although you walk towards me, I remain the same distance from you. What am I?

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.