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 
See Also
| 1951 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 24 |
Followed by Problem 26 | |
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