Can you solve below mathematical equation?

2^1234 - 2^1233

A man who was outside in the rain without an umbrella or hat didn’t get a single hair on his head wet. Why?

You visit a home for specially-abled children on the occasion of Christmas where you meet with 50 children. You have a box of chocolates containing 50 chocolates exactly.

What if you were asked to one chocolate to each child in a manner that one chocolate still remains in the box? Is it possible?

What is black when you buy it, red when you use it, and gray when you throw it away?

There is a square piece of paper with a hole that is denoted by the circle on the top right side in the given picture. You have to cut the paper in a manner that it forms two and only two separate pieces of paper and then rearrange the pieces in a manner that the holes come in the centre of the paper.

You throw me out when you want to use me and you take me in when you don't want to use me.

Who Am I?

After teaching his class all about Roman numerals (X = 10, IX=9 and so on) the teacher asked his class to draw a single continuous line and turn IX into 6. The teacher's only stipulation was that the pen could not be lifted from the paper until the line was complete.

Katniss and Peeta are liars. They both lie on some specific days.

Katniss lies on Fridays, Saturdays and Sundays. She speaks the truth on all other days.

Peeta lies on Tuesdays, Wednesdays and Thursdays. He speaks the truth on all other days.

Can you tell that one day of the week when both of them will say "Tomorrow, I will lie."?

What brings you down but never up?

How can you throw a ball as hard as you can and have it come back to you even if it doesn't hit anything there is nothing attached to it and no one else catches or throws it.