There are 20 people in an empty, square room. Each person has full sight of the entire room and everyone in it without turning his head or body, or moving in any way (other than the eyes). Where can you place an apple so that all but one person can see it?

What do the following words have in common?

Assess
Banana
Dresser
Grammar
Potato
Revive
Uneven
Voodoo

I am five letter word that is under you.
If you remove my 1st letter, then I am over you.
If you remove my 1st and 2nd letters then I am all around you.

Who am I?

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

Alex is stranded on an island covered in forest.
One day, when the wind is blowing from the west, lightning strikes the west end of the island and sets fire to the forest. The fire is very violent, burning everything in its path, and without intervention the fire will burn the whole island, killing the man in the process.

There are cliffs around the island, so he cannot jump off.

How can the Alex survive the fire? (There are no buckets or any other means to put out the fire)

What can you catch but never throw?

It belongs to you, but other people use it more than you do. What is it?

A professor thinks of two consecutive numbers between 1 and 10.
'A' knows the 1st number and 'B' knows the second number

A: I do not know your number.
B: Nor do I know your number.
A: Now I know.

What are the four solutions for this?

You are trapped into a death trap by the famous jigsaw killer. As usual, a screen flashes in front of you and explains you the trap game. There are 100 pearls kept in a bowl in front of you and an empty bowl. Among the 100 pearls, 50 are white and 50 are black. You can divide them as you like into the two bowls. Once you are done, you will pull a lever, which will turn the room pitch black. The bowls will move and shuffle around. In the dark, you have to pick up one pearl from any bowl. Once you do that, the room will flood with lights again. If the peral you have in your hand is white, you will be allowed to live, but if the pearl you picked is black, the room will be filled with poisonous gas and you will die. How will divide the pearls to increase your chances of survival?

There is a box in which distinct numbered balls have been kept. You have to pick two balls randomly from the lot.

If someone is offering you a 2 to 1 odds that the numbers will be relatively prime, for example
If the balls you picked had the numbers 6 and 13, you lose $1.
If the balls you picked had the numbers 5 and 25, you win $2.

Will you accept that bet?