Why 1729 is a magic number? Answer Logically.

The more you take me, the more you leave me behind.
Who Am I?

What is more useful when it is broken?

What does this below rebus puzzle mean?

Solve the equation in the image by looking at the pattern closely.

Five thieves looted a bank and they ran away in a car. The bank staff informed the police and they began the search of their car in their jeep. They found them on a road and chased them eventually catching them. The light that is used to fill the number plate was broken on the thieves' car. Also, the headlights of the jeep police were not working. How were the police able to catch the thieves then?

All of the flowers I have are orchids except two. All of the flowers I have are hibiscuses except two. All of the flowers I have are roses except two.

Can you tell me how many flowers I have?

When I got four, I have it none.
When I got two, I have it some.
When I got none, I have it all.

What is it?

Mr Black, Mr Gray, and Mr White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr Black, who hits his shot 1/3 of the time, gets to shoot first. Mr Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr Black, where should you shoot first for the highest chance of survival?

Can you solve below mathematical equation?

2^1234 - 2^1233