Why 1729 is a magic number? Answer Logically.

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

A Japanese ship is sailing in the Indian Ocean. The captain of the ship feels tired and decides to take shower to be rejuvenated. He goes to take the shower after keeping his diamond-studded Rolex watch and gold chain on the table.
When he comes back after 15 minutes, he finds them missing. There are 4 crew members on the ship and he calls them one by one to ask them what they were doing in that duration.

Following are the answers:
1. Crew 'A' who is the cook replies that he was cooking mutton for the crew members.
2. Crew 'B' who is a housekeeper tells that he was sleeping in his room.
3. Crew 'C' who is the engineer says that he was checking on the generator.
4. Crew 'D' who is another housekeeper says that he was correcting the hoisted flag that was put upside down.

It took only a couple of seconds for the captain to find the thief. Can you find the thief too?

There are 20 people in an empty, square room. Each person has full sight of the entire room and everyone in it without turning his head or body, or moving in any way (other than the eyes). Where can you place an apple so that all but one person can see it?

You walk into a room where there are three primates held in their respective cages:
1) A lion who is eating the flesh of a goat.
2) An orangutan who is playing with blocks.
3) A donkey who is sitting idle.

Who is the most intelligent primate in the room?

Take away my first letter, then take away my second letter. Then take away the rest of my letters, yet I remain the same. What am I?

Can you find the missing letter in the sequence?
S - T - I - L - ? - T - F - Y - C

Sherlock Holmes was challenged to make a pre-drawn line smaller without erasing it. He did it in fractions of seconds. How?

A Man gave one of his sons 10 cents and another son was given 15 cents. What time is it?
Hint: Figure out the relation between time and number, is not so easy..:)

Can you find the missing piece of the Porsche?