Complete the given grid with valid words. You can only use the letters AAEEIIMMPPTT.

Hint: The grid reads the same across as down.

I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?

I am a prime number.
The double of myself is equal to the square of me.

which number am I?

Can you find out the number that should replace the question mark with a valid reason?

Which city is three-fifths chick two third cat and 50% goat?

Irene killed hundreds of people mercilessly and yet the police were not able to put her behind the bars. Why?

I have no life, but I can die. What am I?

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?

Okay before we begin with the puzzle, do keep in mind that you have to answer it quickly.

You are participating in a car race. Seeking the perfect moment, you overtake the second person in the race. What positions are you in now?

I am the fastest animal but cannot climb the tree. What am I?