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

In the attached figure, you can see a chessboard and two rooks placed on the chess board. What you have to find is the number of squares that do not contain the rooks. How many are there?

What is both possible and impossible at the same time?

Can you find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours.

A chicken farmer has figured out that a hen and a half can lay an egg and a half in a day and a half. How many hens does the farmer need to produce one dozen eggs in six days?

Identify Me

Hint1: I am a god
Hint 2: I am a planet
Hint 3: measurer of heat

You can take four of the five letters out of this word, but the pronunciation never changes. What is the word?

You are stuck on an island where you have nothing. You find four pieces of paper somewhere on the island. What will be your strategy to escape from the island safely?

PS: No other resource is available to you on the island, neither can you build anything.

A bomb goes off.
Carnage.
One person, only a few feet away, survives! How can this be?

One absent-minded ancient philosopher forgot to wind up his only clock in the house. He had no radio, TV, telephone, internet, or any other means for telling time. So he travelled on foot to his friend's place a few miles down the straight desert road. He stayed at his friend's house for the night and when he came back home, he knew how to set his clock. How did he know?