Can you replace the question mark with the correct number in the below table sequence?

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

You are trapped in a room with two doors. One leads to certain death and the other leads to freedom. You don't know which is which.
There are two robots guarding the doors. They will let you choose one door but upon doing so you must go through it.
You can, however, ask one robot one question. The problem is one robot always tells the truth, the other always lies and you don't know which is which.
What is the question you ask?

A beggar on the street can make one cigarette out of every 6 cigarette butts he finds. After one whole day of searching and checking public ashtrays the beggar finds a total of 72 cigarette butts. How many cigarettes can he make and smoke from the butts he found?

There is a square of a particular number which when doubled, becomes 7 more than its quarter.

Can you find the number?

You have two strings whose only known property is that when you light one end of either string it takes exactly one hour to burn. The rate at which the strings will burn is completely random and each string is different. How do you measure 45 minutes?

How many points are there on the globe where, by walking one mile south, then one mile east and then one mile north, you would reach the place where you started?

I am a type of food that is often found in the fridge and can be white in colour. What I am?
Hint 1: I am a dairy product.
Hint 2: You can spread me on the bread.

What is full of holes but still holds water?

Can you place three balls such that the equation shown in the picture holds true?