Can you find a number that lies one third of the distance between 1/3 and 2/3?

On a magical land of Mexico , all the animal in the land are rational.

There are 10 tigers and one goat.
Tiger can eat goat but since it's a magical land , the tiger who eats the goat , turns into goat and then can be eaten by the remaining tiger(s).

If we leave them for some time then how many goat and tiger will be there , when we come back ?

There was a competition where the contestants had to hold something. At the end of the event, the winner was a person who had no hands or feet. What was it that the contestants had to hold?

Decode below three cipher riddles:

26 L of the A
7 D of the W
1000 Y in a M

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

An American nightclub called 'The Coconut Grove' had a terrible fire in which over 400 people died. A simple design flaw in the building led to a high death toll. Subsequently, regulations were changed to ensure that all public buildings throughout the country eliminated this one detail, which proved deadly. What was it?

If,
9 * 8 * 7 = 65
8 * 7 * 6 = 50
7 * 6 * 5 = 37

Find
6 * 5 * 4 = ?

When I get multiplied by any number, the sum of the figures in the product is always me. What am I?

If you’ve got me, you want to share me; if you share me, you haven’t kept me. What am I?

A professor thinks of two consecutive numbers between 1 and 10.
'A' knows the 1st number and 'B' knows the second number

A: I do not know your number.
B: Nor do I know your number.
A: Now I know.

What are the four solutions for this?