Problem
COM-B1-M09-P005 Nine Participants
#5
★☆☆☆☆ Level 1 of 5
In a group of \(9\) people, each person states the number of acquaintances in the group. Prove that the sum of the stated numbers is even.
Each acquaintance pair is counted twice.
Build the acquaintance graph. Each acquaintance pair contributes \(1\) to each of two people, hence \(2\) to the total sum. Therefore the sum of all stated numbers is twice the number of acquaintance pairs and is even.
Translating a word situation into a graph.