MathDB
Shaking hands in a room containing N people

Source: 1978 AHSME Problem 16

June 6, 2014
AMC

Problem Statement

In a room containing NN people, N>3N > 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?
<spanclass=′latex−bold′>(A)</span>0<spanclass=′latex−bold′>(B)</span>1<spanclass=′latex−bold′>(C)</span>N−1<spanclass=′latex−bold′>(D)</span>N<spanclass=′latex−bold′>(E)</span>none of these<span class='latex-bold'>(A) </span>0\qquad<span class='latex-bold'>(B) </span>1\qquad<span class='latex-bold'>(C) </span>N-1\qquad<span class='latex-bold'>(D) </span>N\qquad <span class='latex-bold'>(E) </span>\text{none of these}
Back to ProblemsView on AoPS