hosted a dinner with 10 guests, not including myself. whenever two guests talked for the first time, they shook hands. after the party, every guest (not including myself) had shaken a different number of hands. for example, if the first guest shook 3 hands, then no other guest shook exactly three hands. how many hands did i shake? (nobody shook the same hand twice, and if a guest shook my hand they included it in their count.)