A father's child, a mother's child, yet no one's son.

Who am I?

I am beautiful, up in the sky. I am magical, yet I cannot fly. To people I bring luck, and to some people, riches. The boy at my end does whatever he wishes. What am I?

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?

What breaks yet never falls, and what falls yet never breaks?

Give it food and it will live; give it water and it will die.

What brings you down but never up?

What is the centre of gravity?

Different lights make me strange by changing me into different sizes. What am I?

10 people came into a hotel with 9 rooms and each guest wanted his own room. The bellboy solved this problem.
He asked the tenth guest to wait for a little with the first guest in room number 1. So in the first room, there were two people. The bellboy took the third guest to room number 2, the fourth to number 3, ..., and the ninth guest to room number 8. Then he returned to room number 1 and took the tenth guest to room number 9, still vacant.
How can everybody have his own room?

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).