Football tournament - Argentina TST 2010
Source:
May 2, 2010
combinatorics unsolvedcombinatorics
Problem Statement
In a football tournament there are teams, each of which plays exacly one match against every other team. If a team defeats team , then is awarded points and gets points. If they end up in a tie, they receive point each.
It turned out that in this tournament, whenever a match ended up in a tie, the two teams involved did not finish with the same final score. Find the maximum number of ties that could have happened in such a tournament.