Can you solve below mathematical equation?

2^1234 - 2^1233

Prove that the below maths equation is true.

8 + 8 = 91

A boy and a girl are sitting on the porch.
"I'm a boy," says the child with black hair.
"I'm a girl," says the child with red hair.
If at least one of them is lying, who is which?

How can a man go eight days without sleep?

How many points are there on the globe where, by walking one mile south, then one mile east and then one mile north, you would reach the place where you started?

Imagine you are in a room with no windows or doors. How will you get out?

If you go to the movies and you're paying, is it cheaper to take one friend to the movies twice, or two friends to the movies at the same time?

What kind of band never plays music?

Can you complete the sequence puzzle?

AR TA GE CA LE VI LI _

A woman is sitting in her hotel room and hears a knock at the door. She opens the door to see a man whom she’s never met before. He says, “I’m sorry, I have made a mistake, I thought this was my room.” He then goes down the corridor and into the elevator. The woman goes back into her room and calls security. What made the woman so suspicious of the man?