I have branches, but no fruit, trunk or leaves. What am I?

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.

I am lying and I always lie. Tell me whether I am lying or telling the truth.

The person who makes it has no need for it; the person who buys it has no use for it. The person who uses it can neither see nor feel it. What is it?

You are in a land where thirty men and two women were dressed in classic black and white dresses.
They begin to fight as soon as any of them move.

Where are you?

How much will a 38° angle measure when looked at under a microscope that magnifies ten times?

I travel all around the world but always stay in the corner. What am I?

It can't be seen, can't be felt, can't be heard, and can't be smelt.
It lies behind stars and under hills, And empty holes it fills.
It comes first and follows after, Ends life, and kills laughter.
What is it?

Speaking of rivers, a man calls his dog from the opposite side of the river. The dog crosses the river without getting wet, and without using a bridge or boat. How?

The host of a game show, offers the guest a choice of three doors. Behind one is a expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?