What number when divided in half becomes zero?

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

You can find some missing letters in the picture. By placing two particular letters in the spaces, you can form a nine lettered word beginning from one of the corners and going clockwise direction to the middle. Can you find out the letters and the word?

After teaching his class all about Roman numerals (X = 10, IX=9 and so on) the teacher asked his class to draw a single continuous line and turn IX into 6. The teacher's only stipulation was that the pen could not be lifted from the paper until the line was complete.

No one wants to have it, but if one got it, he does not want to lose it. What is It?

The owner of a popular clothing store comes up with his own method of pricing items. A vest costs $8, socks cost $10, a tie costs $6, and a blouse costs $12. Using the owner’s method, how much would a pair of underwear cost?

What is the largest amount of money that you can possess in change and still if someone asks you for a dollar, you won't be able to give?

Can you name any English verb that becomes its past tense by simply rearranging the alphabets ?

Who is that with a neck and no head, two arms and no hands? What is it?

A donkey is behind another donkey
I'm behind that second donkey
But there is a whole nation behind me

It is a murder you can describe in a word.