Bangladesh Mathematical Olympiad 2015, Secondary, P4
Source: Bangladesh Mathematical Olympiad 2015, Secondary, P4
March 31, 2015
national olympiadgraph theorycombinatorics unsolvedcombinatorics
Problem Statement
There are participants at a BdMO event. Some of the participants shook hands with each other. But no two participants shook hands with each other more than once. Each participant recorded the number of handshakes they made. It was found that no two participants with the same number of handshakes made, had shaken hands with each other. Find the maximum possible number of handshakes at the party with proof. (When two participants shake hands with each other, this will be counted as one handshake.)