Home /
Expert Answers /
Algebra /
in-a-sports-tournament-involving-n-teams-each-team-plays-every-other-team-exactly-once-at-the-end-pa818
(Solved): In a sports tournament involving N teams, each team plays every other team exactly once. At the end ...
In a sports tournament involving N teams, each team plays every other team exactly once. At the
end of every match, the winning team gets 1 point and the 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:
x_(1)>=x_(2)>=cdots>=x_(N).
Prove that for any 1<=k<=N,
(N-k)/(2)<=x_(k)<=N-(k+1)/(2)