Can you solve below mathematical equation?

2^1234 - 2^1233

A man is walking down a road with a basket of eggs. As he
is walking he meets someone who buys one-half of his eggs
plus one-half of an egg.
He walks a little further and meets another person who buys
one-half of his eggs plus one-half of an egg.
After proceeding further he meets another person who buys
one-half of his eggs plus one half an egg. At this point, he
has sold all of his eggs, and he never broke an egg.
How many eggs did the man have to start with?

Assume the given figure to be a delicious doughnut. Yes, now you can concentrate more on the puzzle. So you have this delicious doughnut in your refrigerator when your friends come knocking at the door. There are eight of them. Now you have to make three cuts in this doughnut so that each one of you nine people can enjoy a piece of it. Neither you nor your friends would mind the size of their piece as long as they are getting it. How will you do it?

In the image below, you can see two glasses and two matchsticks.You need to move four matchsticks in such a manner that the crosses come inside the glasses. Note: you cannot move the crossed.

Can you solve the below algebraic mathematical equation?

(J+O+I+N+T)3 = JOINT

As shown in the image, the nine Dogs are square fenced. By constructing just two square fences can you make sure that two Dogs cannot meet each other without crossing the fence?

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?

I am working in a bus company. The company recently went under expansion and therefore there was not enough room for all the buses. As a result, twelve buses had to be stored outside.

If the company decides to expand the garage space by forty percent, enough space to accommodate the current buses will be created leaving enough space for twelve more buses if the need arises in future.

Can you calculate the number of buses that the company owns at present?

There once were seven dwarfs who were all brothers. They were all born two years apart. The youngest dwarf is seven years old. How old is his oldest brother?

A large container is kept in open under the rain. Every passing hour, the water collected inside the container becomes double what it was.

In ten hours, the container is filled completely. Can you calculate how long would it have taken to be filled in half?