What will you call your mother's brother's brother-in-law?

Find The Next Number in this series.
1, 2, 6, 42, 1806 ?

There is a wide field of corn. A goose finds its way into the field and starts running. Can you find out till which point the goose can run into the field?

Intelligence Agency need to break the vault but the problem is that they are not able to break the vault.

On the vault, a text is written as:

31 11 33 33 43 45
21 25
31 24 11 31 51 41

To Break the code Intelligence Agency brings a mathematician named Joseph.
Minutes later he deciphers the code.

Whats the code?

What is the word or phrase?

The peacock is a bird that does not lay eggs. How do they get baby peacocks?

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?

Below the four parts have been reorganised. The four partitions are exactly the same in both arrangements. Why is there a hole?

A solo dice game is played. In this game, upon each turn, a normal pair of dice is rolled and the score is calculated not by adding the numbers but multiplying them.

In a particular game, the score for the second roll is five more than what was achieved in the first roll. The score for the third roll is six less than what was completed in the second roll. The score for the fourth roll is eleven more than what was achieved in the third. The score for the fifth roll is eight less than what was completed in the fourth.

Can you calculate the score for each of the five throws?

Three people enter a room and have a green or blue hat placed on their heads. They cannot see their own hat but can see the other hats.
The colour of each hat is purely random. They could all be green, blue, or any combination of green and blue.
They need to guess their own hat colour by writing it on a piece of paper, or they can write 'pass'.
They cannot communicate with each other in any way once the game starts. But they can have a strategy meeting before the game.
If at least one of them guesses correctly they win $10,000 each, but if anyone guesses incorrectly they all get nothing.
What is the best strategy?