Difference between revisions of "1978 AHSME Problems/Problem 16"

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1978 AHSME Problems/Problem 16
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==Problem==
 
==Problem==
 
In a room containing <math>N</math> people, <math>N > 3</math>, at least one person has not shaken hands with everyone else in the room.  
 
In a room containing <math>N</math> people, <math>N > 3</math>, at least one person has not shaken hands with everyone else in the room.  

Latest revision as of 14:17, 18 June 2021

Problem

In a room containing $N$ people, $N > 3$, at least one person has not shaken hands with everyone else in the room. What is the maximum number of people in the room that could have shaken hands with everyone else?

$\textbf{(A) }0\qquad \textbf{(B) }1\qquad \textbf{(C) }N-1\qquad \textbf{(D) }N\qquad  \textbf{(E) }\text{none of these}$

Solution

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