2, 3, 5, 9, 17, _ What is the next number in the sequence?

A few friends are enjoying their sea voyage in a boat full of apples. On the way, they felt hungry and thus decided to eat the apples. Together, they ate two dozen of apples. When they have eaten the apples, will there be any change in the water level?

You are given four results as below:
1111 = F
2222 = E
3333 = T
Then, can you find out how to code 4444?

A woman lives in a Tall building thirty-six floors high and served by several elevators which stop at each floor going up and down. Each morning she leaves her apartment and goes to one of the elevators. Whichever one she takes is three times more likely to be going up than down. Why?

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?

At a party, there are five people and a whole round cake lying at the centre of the table. Only four people will make a cut and take their piece and the last one will get the remaining piece on the table. How can they make sure that everyone gets a 1/5th of the piece?

If,

6 / 7 = 2
3 / 9 = 7
8 / 2 = 6

Then

4 / 5 = ?

One is to three as three is to five and five is to four and four is the magic number.
What is the pattern?

I have Rs.50 and I spend it in the way as below.

An office is divided into 8 cubicles. How many of the cubicles are painted if only 1/8 of the cubicles are painted?