Can you find out the next digit in the following series ?

0, 0, 1, 3, 2, 6, 3, 9, 4, 12, 5, ?

A horse was tied to a rope 5 meters long and the horses food was 15 meters away from the horse. How did the horse reach the food?

Pronounced as one letter,
And written with three,
Two letters there are,
And two only in me.
I am double, I am single,
I am black blue and grey,
I am read from both ends,
And the same either way.

An evil man kidnapped someone and made them take one of two pills. One was harmless, but the other was poisonous. Whichever pill the victim took, the kidnapper took the other one. The victim took their pill with water and died. The kidnapper survived. How did the kidnapper get the harmless pill?

Find three numbers such that

* When we multiply three numbers, we will get the prime numbers.
* The difference between the second and the first number is equal to the third and second.

Why 1729 is a magic number? Answer Logically.

I am five letter word that is under you.
If you remove my 1st letter, then I am over you.
If you remove my 1st and 2nd letters then I am all around you.

Who am I?

John: "Hi Teacher, What is your favourite movie ?".
Chemistry Teacher: "Indium Cerium Platinum Iodine Oxygen Nitrogen".
Ten seconds later... John replied I got it.

Do you?

I never was there, I am always to be.
You have never ever seen me, not ever you will.
Yet I am the confidence of everyone.

Who Am I?

When Jack was six years old he hammered a nail into his favourite tree to mark his height. Ten years later at age sixteen, Jack returned to see how much higher the nail was. If the tree grew by five centimetres each year, how much higher would the nail be?