In a sports tournament involving N teams, each team plays every other team exactly one. At the end of every match, the winning team gets 1 point and losing team gets 0 points. At the end of the tournament, the total points received by the individual teams are arranged in decreasing order as follows: x1≥x2≥⋯≥xN.
Prove that for any 1≤k≤N, 2N−k≤xk≤N−2k+1 combinatoricsTournamentgraph theoryISI 2024