Can you solve below mathematical equation?

2^1234 - 2^1233

A number can be multiplied by multiple of nine
i.e 9 18 27 36 45 ...

and the resulting number consist of only one digit.

Can you identify the number ?

Before the start of the car race, John and Jacob have the same amount of fuel in their car. With this fuel, John can drive for 4 hours while Jacob can drive five hours.
After a time they realize that the amount of fuel left in John's car is 1/4th of the fuel in Jacob's.

For how long they are racing?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

A girl has as many brothers as sisters, but each brother has only half as many brothers as sisters. How many brothers and sisters are there in the family?

Can you find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours.

Baseball bat and ball cost $100. If the bat cost $99 more than the ball, what is the cost of each?

Rectify the following equality 101 - 102 = 1 by moving just one digit.

All of Jacob's shoes are red except two.
All of Jacob's shoes are green except two.
All of Jacob's shoes are yellow except two.

How many shoes does Jacob have?

John can eat 27 chocolates in an hour, Jacob can eat 2 chocolates in 10 minutes, and Jolly can eat 7 chocolates in 20 minutes. How long will it take them to share and eat a box of 120 chocolates whilst playing Chess?