Can you find a number that lies one third of the distance between 1/3 and 2/3?

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?

There were three women in all the swimming costumes!
One was happy and the other two were sad!
The happy one was crying and the sad ones were smiling.
Why was this?

These types of puzzles are known as charades. What you have to do is to find two words that are referred to in the first stanza and the second stanza and put them together to form the third word in the third stanza.

Just for example, if my first refers to 'off' and my second refers to 'ice', then my whole will be the 'office'.

My first is present - future's past -
A time in which your lot is cast.

My second is my first of space
Defining people's present place.

My whole describes a lack of site -
A place without length, breadth, or height.

There is a family that live in a round house. The two parents go out for a movie and leave a babysitter to watch their son. They come back and the kid was not there. Some one kidnapped him. The maid said she was cleaning in a corner. The cook said he was making pizza. The babysitter said she was getting a board game. Who kidnapped him.

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?

A river should be crossed by a father, a mother and their two sons and two daughters.
There are some rules that should be followed while crossing the river. There can be only two people in the raft while crossing. The daughters cannot be with their father unless there is the presence of the mother. The sons cannot be with their mothers unless the father is present. Unless the guard is on the board, the criminals cannot be with any of the family members. Only the adults like the father, the guard, and the mother knows to use the raft.

How will they cross the river?

What will be the best approach to finding all the prime numbers less than 75 that leave an odd reminder when we divide them with 5?

Can you count the number of lines in the below picture?

I have a mouth but I don't eat.
I have a bank but have no money.
I have a bed but i dont sleep.
I wave but have no hands.

Who Am I ?