There is one thing that goes round the house and also inside the house but never even share a brief touch. What is it?

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?

John was so frustrated to be the suspect of being a sleeper terrorist that he shoot himself right between the eyes with a revolver in his toilet. The revolver and the bullets were accurate. Minutes later John walks out of the toilet unharmed.
How can this be possible?

There is an English word that can be used up to four times in a row without modifying the spelling and form a valid grammatical sentence.

Do you know what word is that?

There are two words one resembles the "state of rest" and the other is related to "writing/reading material".

Can you name these two words which also sound similar?

Can you place six X (crosses) in below board without making three in a row in any way ?

Consider this about a word: The first two letters signify a male, the first three letters signify a female, the first four letters signify a great, while the entire world signifies a great woman. What is the word?

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 ?

A man is trapped in a room. The room has only two possible exits doors. Through the first door there is a room constructed from magnifying glass. The blazing hot sun instantly fries anything or anyone that enters. Through the second door there is a fire-breathing dragon. How does the man escape?

At a party, there are five people and a whole round cake lying at the centre of the table. Only four people will make a cut and take their piece and the last one will get the remaining piece on the table. How can they make sure that everyone gets a 1/5th of the piece?