1951 AMC 12 Problem 31
Attempt Problem 31 of the 1951 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1951 AMC 12 solutions, or check the answer key.
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31.
A total of handshakes was exchanged at the conclusion of a party. Assuming that each participant was equally polite toward all the others, the number of people present was:
Answer: D
Small hint:
With people, each unordered pair shakes hands once
Big hint:
Solve
Solution:
With people the number of handshakes is Thus and the positive solution is
Thus, the correct answer is D.