27 handshakes of m x n students (HOMC 2018 Ind. p13)
Source:
January 31, 2020
combinatorics
Problem Statement
A competition room of HOMC has students where are integers larger than . Their seats are arranged in rows and columns. Before starting the test, every student takes a handshake with each of his/her adjacent students (in the same row or in the same column). It is known that there are totally handshakes. Find the number of students in the room.