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

Can you solve this amazing hard number series problem?
7, 8, 10, 12, 16, 18 ?

A cat, a dog and a monkey were stolen. 3 suspects got caught: Harish, Manoj and Tarun. All we know is each person stole one animal, but we do not know who stole which. Here are the investigation statements. Harish said: Tarun stole the cat. Manoj said: Tarun stole the dog. Tarun said: They both were lying. I did not steal the cat or the dog. Later on, the police found out the man who stole the monkey told a lie. The man who stole the cat told the truth. Can you find out who stole which?

If,
9 * 8 * 7 = 65
8 * 7 * 6 = 50
7 * 6 * 5 = 37

Find
6 * 5 * 4 = ?

John has eleven friends. He has a bowl containing eleven apples. Now He wants to divide the eleven apples among his friends, in such a way that an apple should remain in his bowl.
How can He do it?

P is the father of Q and S is the son of R. T is the brother of P and has a daughter U. If R is the sister of P, then what is the relation between U, Q and S?

Next Number in the Series,

5, 16, 49, 104, ?

There are a hundred statements.

First person says: At least one of the statements is false.

Second person says: At least two of the statements is false.

Third person says: At least three of the statements are false.

Fourth person says: At least four of the statements are false.

..

..

..

Hundredth person says: At least a hundred of the statements are false.

Analysing it, how many statements do you think are false and how many are true?

Two fathers and two sons decided to go to a shop and buy some sweets upon reaching. Each of them bought 1 kg of sweet. All of them returned home after some time and found out that they had 3kg of sweets with them.

They did not eat the sweets in the way, nor threw or lose anything. Then, how can this be possible?

Which digit occurred maximum times between the number 1 and 1000?