There is a unique number which when multiplied by any number from 1 to 6, we will get the new number that contains the same digits only.

Can you find that number?

Find out a multi-digit number that if multiplied by the number 9 or any of its multiplications products (i.e. 18, 27, 36, 45,..) will result in the multiplication factor repeated (n) number of times.

What number does the below three word/phrase identify and why?
1. Deck
2. Year
3. Singing in the Rain

I am white when I am dirty, and black when I am clean. What am I?

A farmer and his neighbour once went to Emperor Akbar"s court with a complaint. "Your Majesty, I bought a well from him," said the farmer pointing to his neighbour, "and now he wants me to pay for the water."
"That"s right, your Majesty," said the neighbour. "I sold him the well but not the water!"?
The Emperor asked Birbal to settle the dispute. How did Birbal solve the dispute?

Why Wine Glass Stem is so long?

On my way to St. Ives I saw a man with 7 wives. Each wife had 7 sacks. Each sack had 7 cats. Each cat had 7 kittens. Kittens, cats, sacks, wives. How many were going to St. Ives?

There are two insects on a tile. Insect X is sitting on one side of the tile (point A) and Insect Y is sitting opposite on the other side of the tile (point B). Now both of them decide to change their position and thus X starts crawling to point B and Y starts crawling to point A. When they meet and pass each other in between, X takes 20 seconds to reach B and Y takes just 5 seconds to reach A.

Can you calculate the total time each of the insects took to change their positions?

If,

6 / 7 = 2
3 / 9 = 7
8 / 2 = 6

Then

4 / 5 = ?

I sleep during the day and fly at night, but I have no feathers to aid my flight. What am I?