Can you solve below mathematical equation?

2^1234 - 2^1233

Begin with a word, five letters to my name,
Remove the first and last but I am the same
Take out my middle and still, I remain.
What word am I?

A donkey is behind another donkey
I'm behind that second donkey
But there is a whole nation behind me

It is a murder you can describe in a word.

Solve the alphametic puzzle by replacing the alphabet with the number.

S T O R M +
S O L E S
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In a kingdom, King George did not allow any citizen to visit the world outside. Also, only a person with proper paperwork was allowed to enter or he was sent back. A wooden bridge was what connected the kingdom to the world. The king had appointed a sharpshooter who would check the every five minutes on the bridge to check. After checking, he would go back to his hut and return exactly after five minutes again. The bridge took 9 minutes to cross.

A merchant was able to escape the kingdom without harming the shooter. How?

In front of you, there are 9 coins. They all look absolutely identical, but one of the coins is fake. However, you know that the fake coin is lighter than the rest, and in front of you is a balance scale. What is the least number of weightings you can use to find the counterfeit coin?

It spends most of its day eating white, but when it’s quick enough, it gets to eat fruit and sometimes some blue things. It’s in a dark room, where the walls are blue, it runs from a ghost that roams the halls and haunts it all the time. What is it?

Twenty frogs are sitting on a log floating on the surface of a river. Two of them decide to jump off into the water.

How many frogs are there on the log at this moment?

Manish and Manoj play 5 games of chess.
Both Manish and Manoj win the exact same number of games. There is no tie at all.

How?

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?