1951 AHSME Problems/Problem 31
Problem
A total of handshakes were exchanged at the conclusion of a party. Assuming that each participant was equally polite toward all the others, the number of people present was:
Solution
The handshake equation is , where
is the number of people and
is the number of handshakes. There were
handshakes, so
The factors of
are:
.
As we can see, only
fit the requirements
if
was an integer.
Therefore, the answer is