Question: You need to organize a football tournament. There are n teams given. You need to prepare a schedule for the matches so that each team plays with every other team and on the same day no team plays twice. You want to finish the tournament as early as possible.Give schedule for tournament.

Solution: If n is the number of competitors, a pure round robin tournament requires n*(n-1)/2 games. If n is even, then in each of (n − 1) rounds, n/2 games can be run in parallel, If n is odd, there will be n rounds with(n-1)/2 games, and one competitor having no game in that round.
The standard algorithm for round-robins is to assign each competitor a number, and pair them off in the first round
Round 1. (1 plays 14, 2 plays 13, ... )
1 2 3 4 5 6 7
14 13 12 11 10 9 8
then fix one competitor (number one in this example) and rotate the others clockwise …
Round 2. (1 plays 13, 14 plays 12, ... )
1 14 2 3 4 5 6
13 12 11 10 9 8 7
ound 3. (1 plays 12, 13 plays 11, ... )
1 13 14 2 3 4 5
12 11 10 9 8 7 6
until you end up almost back at the initial position