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?