1951 AHSME Problems/Problem 31
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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 30 |
Followed by Problem 32 | |
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