At the faculty costume party , each teacher from Transylvania Middle school came dressed as his of her favorite creepy creature . The teachers arrived one at a time , and when a new teacher came in , each of the teachers already there lined up at the door and shook hands with newcomer . Count Dracula (Mr.Blab, the math teacher) kept track of the # of handshakes exchanged . He said that there were 171handshakes exchanged at the party . How many teachers came to the costume party.

Question

0,1,3,9,15,17,19 are my answer's

Answer 1

n(n-1)/2 = 171
Since 342 = 18*19, there were 19 teachers.