Classic Hand shake question I am asked the following question:


  My wife and I were invited to a party attended by four other
  husband-wife couples, making a total of ten people. As people arrived,
  there was some hand shaking. No one shook their own hand, and there
  were no husband-wife hand shakes. When it was over, I asked each
  person "How many people did you shake hands with?" I asked nine people
  (not including myself) and got nine different answers. How many people
  did my wife shake hands with?


Since there are 10 people in the room should I use the formula n(n-1)2, which results in 10(10-1)/2=45 which would be the sum of all the handshakes. If I divide that by ten I would get 4.5 people shook his wife's hand.

This doesn't seem correct at all. What is the right direction to head in order to solve this question?

EDIT:

I ended up trying to solve by pairing everyone together and drawing a graph showing the relations between everyone:

But this wasn't complete apparently.
Hint:  No person shook more than eight hands, so you must have gotten answers from 0 to 8 inclusive.  Who is married to the person who shook 8?
The answer lies in the question itself.
It says, there were no hand shakes between husband-wife and the man asking everyone has not included himself in the count, so he and his wife would not be counted.
Therefore the answer is 8...His wife shook hands with 8 people(excluding her husband).