Why 1729 is a magic number? Answer Logically.

A journalist was investigating a sacred cult in the jungles of Africa when he was caught by one of the person. He was confined in a cave till the leader arrived. The leader told him that he need to tell him a statement. If he thinks the statement is true, then the journalist head will be chopped off. If he thinks that the statement is false, his head will be smashed with a hammer.

What statement did the journalist make to survive?

John and Jill are madly in love with each other. To remind Jill of his pure love, John wants to send her a ring by post but in their country where burglary is quite prominent, any package that is not locked comes under the risk of being stolen for the contents.

John and Jill possess many padlocks but neither one of them has the other key.

Can you find a way John can send the ring to Jill safely?

If,
29 - 1 = 30
9 - 1 = 10
14 - 1 = 15

Based on similar logic, Can you prove that the below algebraic equation is true?
11 - 1 = 10 ?

Can you quickly find which two matchstick figures are identical?

You have to fill the below given grid in a manner that every row and column contains the digits 1 to 6. Also, make sure that the squares that are connected with each other must contains the same digit.

Forwards I am heavy, backward I am not. What am I?

My location can be determined by the below rebus.
So where am i ?

The following alphametic has only one solution. Can you find it?
ENLIST + SILENT + LISTEN = ANAGRAM

PS: You may start the number from 0.

A man is looking at a photograph of someone. His friend asks who it is. The man replies, “Brothers and sisters, I have none. But that man’s father is my father’s son.” Who was in the photograph?