My roommate and I are having a house party. We invite 15 couples. At the party, everyone must shake hands with everyone whom they do not already know. At the end of the party, I can't remember the number of people I have met, so I go ask all other people at the party how many hands they have shaken, and they each tell me a different number. You do not shake hands with yourself or your 'partner' (the person with whom you came). How many hands did my roommate shake?
Please explain how you got the answer.