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

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

In The 1st month of this year(the year 2013), I noticed that the date 13-1-13 (13 January 2013) is special.

This date is special as:

Date * Month = Year.

Can you figure out which year of this century has a maximum number of such dates?

You are trapped into a death trap by the famous jigsaw killer. As usual, a screen flashes in front of you and explains you the trap game. There are 100 pearls kept in a bowl in front of you and an empty bowl. Among the 100 pearls, 50 are white and 50 are black. You can divide them as you like into the two bowls. Once you are done, you will pull a lever, which will turn the room pitch black. The bowls will move and shuffle around. In the dark, you have to pick up one pearl from any bowl. Once you do that, the room will flood with lights again. If the peral you have in your hand is white, you will be allowed to live, but if the pearl you picked is black, the room will be filled with poisonous gas and you will die. How will divide the pearls to increase your chances of survival?

What does it mean?

I am a five-letter word and comprises two different vowels and three same consonants. I am so strong that I can spoil your entire work.

Can you find out who am I?

Can you figure out the logic I used to decide the order of the following words:
gun, shoe, spree, door, hive, kicks, heaven, gate, line, den

Two old friends, Jack and Bill, meet after a long time.

Three kids
Jack: Hey, how are you, man?
Bill: Not bad, got married and I have three kids now.
Jack: That's awesome. How old are they?
Bill: The product of their ages is 72 and the sum of their ages is the same as your birth date.
Jack: Cool..But I still don't know.
Bill: My eldest kid just started taking piano lessons.
Jack: Oh, now I get it.

How old are Bill's kids?

It begins where the time ends.
Its second is an expression of surprise.
Its third is a question.
Its fourth is urinate.
It ends with a drink.

Which country it is?

An old Woman left INR 33,333 to be divided equally among two fathers and two sons and each was to receive INR 11,111.
How was this possible?