What does the following represent?

N N N N N N N

A A A A A A A

C C C C C C C

You can see it everyday, But cannot touch it at will. What is it?

While preparing the table for dinner, wife came up with an idea to tease his mathematician husband. She asked her husband to pick nine toothpicks and make ten without breaking any toothpick.

The husband was also smart and did it within seconds. How ?

You are given 16 witch hats. The hats are divided in four different colours – red, blue, green and yellow. Every colour has been assigned to four hats. Now each of the hat will be glued with a label of an arithmetic sign – ‘+’, ‘-‘, ‘x’ or ‘/’. But you can label one sign only once on one colour. In such an arrangement, the hats can be uniquely defined by its colour and symbol.

Can you arrange all the 16 hats in a 4x4 grid in a fashion that no two rows and columns have a repetition of colour or sign?
We have arranged four hats in the below picture to assist you.

What begins with T, ends with T, and has T in it?

I know a 5-digit number having a property that With a 1 after it, it is three times as large as it would be with a one before it.

Guess the number?

How can you write nineteen in a manner that if we take out one, it becomes twenty?

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 eleven plus two equals one, what does nine plus five equal?

The following alphametic has only one solution. Can you find it?
ENLIST + SILENT + LISTEN = ANAGRAM

PS: You may start the number from 0.