MathDB

10

Part of 2005 Switzerland - Final Round

Problems(1)

n > 10 teams take part in a football tournament

Source: Switzerland - 2005 Swiss MO Final Round p10

12/26/2022
n>10n > 10 teams take part in a football tournament. Every team plays exactly once against each other. A win gives two points, a draw a point, and a defeat no point. After the tournament it turns out that each team gets exactly half their points in the games against the bottom 1010 teams has won (in particular, each of these 1010 teams has won the made half their points against the 99 remaining). Determine all possible values ​​of nn, and give an example of such a tournament for these values.
combinatorics