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?
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.