What is the word or phrase?

For this puzzle, you might have to find logic in something illogical. But hey, it's fun and a healthy little break from your strenuous puzzle-solving sessions.

Can you decipher the meaning in the following cluster of letters?

ITIT,NCENTCENT

The below given figure comprises of a pattern through which you can determine the missing letter. Can you push your mind to find the pattern and add the missing letter?

What can you hold in your right hand, but never in your left hand?

I have nine bottles of wine and one of the nine bottles is poisoned.
I need to find the poisoned bottle with two facts
(1) Poison is deadly, only a sip will cost death
(2) I have two mice to do so.

How should I do it?

If you had a pizza with crust thickness 'a' and radius 'z', what's the volume of the pizza?

A man is found hanging dead from the ceiling of a room. The room’s dimensions are 15 x 15 x 15. The man is only 6ft tall and the rope was only 2ft long. There are no windows and only one door to the room. The door is bolted shut from the inside, and a puddle of water is under the man. How did he kill himself?

Here is what you have to do. You have to throw a ball as hard as you can but it must return back to you even if it does not bounce at anything. Also, you have nothing attached to the ball. There is no one on the other end to catch that ball and throw it back at you.

How will you do it?

Twice ten are six of us,

Six are but three of us,

Nine are but four of us;

What can we possibly be?

Would you know more of us?

Twelve are but six of us,

Five are but four, do you see?

What are we?

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?