What is both possible and impossible at the same time?

The Little ant seems to be always confused. Do you know why?

A man escapes from jail using help from his girlfriend. The investigators suspect four girls of being the man's girlfriend.

Out of those four girls, one is his girlfriend who is lying. Two of the girls are completely innocent and are speaking the truth. One of the girls is the man's sister who is helping the girlfriend lie. Following are the statements from all four of them:

Ariana: "Myrna is his girlfriend."
Jane: "Angelina is lying."
Angelina: "Ariana is lying."
Myrna: "Jane is not his sister."

Can you find out who is the man's sister among them?

During an experiment, a guy throws a bouncy ball from a 100 feet tall building. The ball has a specific characteristic. Every time it hits the ground, it bounces up halfway.

How many bounces do you think the ball will make before it comes to a stop ?

The doctor prescribed you to take one pill from the bottle every half an hour. The bottle is now left with only three pills.

How long do you think you have before you run out of pills?

How many bananas can you eat if your stomach is empty?

A network of 20 x 10 squares is given to you.

Can you calculate how many unique squares and rectangles can be formed combining two or more individual squares ?

If you remove one from eleven, it becomes ten. If you remove one from nine, it becomes ten.

How is this possible?

You need to climb ten stairs. At every stair, you can either take one step up or you can jump two steps up.

In how many different ways you can climb 10 stairs?

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?