Why 1729 is a magic number? Answer Logically.

I start and end with 500 and carry a 5 in my heart. But I require the first letter and the first number to be complete. I am the name of a King.

Who am I ?

A worker is to perform work for you for seven straight days. In return for his work, you will pay him 1/7th of a bar of gold per day. The worker requires a daily payment of 1/7th of the bar of gold. What and where are the fewest number of cuts to the bar of gold that will allow you to pay him 1/7th each day?

In a jungle where there are no street lights or any other artificial source of lights, I notice a black snake crossing the road.
How did I get sight of the snake?

Sweet & very intelligent katty has 8 puppets(Jane Bird Barbie Angel Colleen Nora Lass Missy).
All puppets are of different size. She arrange all puppets to face towards the guest and tell the guess the following clues :

* Jane has three puppets bigger on its left side
* Bird has two puppets smaller on its left side
* Barbie has one puppet bigger on its right side
* Angel has two puppets smaller on its right side
* Colleen has one puppet bigger on its left side
* Nora has one puppet smaller on its left side
* Lass has four puppets bigger on its right side
* Missy has three puppets smaller on its right side

Also some puppets are inside the bigger puppets.

Assuming you are the guest , can you tell the katty how the puppets are arranged ?

4 fathers, 2 grand-fathers and 4 sons went to watch the movie.What is the minimum number of tickets they need to buy ?

Can you find out which number multiplied by itself will give the output as 12345678987654321?

There are 2 people near the river and both of them want to get on the other side. The boat can only take one of them. But they got across.
How?

John is found dead in his office at his desk. The police have narrowed the suspects down to three people: Mrs. Jacob, John’s wife Hena and his business partner Jason . All three visited John on the day of his murder, but all three provide the police with stories of explanation as to the reason for their visit.
Police found John with his wrist watch still on his right arm, a torn up picture of his wife laying on the floor beside the trash can, and an ink pen in his right hand. On the desk, the police found a name plate, a telephone that was off the hook, and a personal calendar turned to the July 5th page with 7B91011 written on it. After examining this evidence, the police knew their suspect. Who was it ?

You see a mathematical expression in the picture. Can you think of a movie that this expression refers to?