❔ A football tournament has 66 teams competing and organized in a single-elimination format (the loser of each match is immediately eliminated from the competition). How many matches will be played in total to determine the final winner?
This problem might seem like it requires a complex solution, but it turns out to have an elegant one, and this solution can even be generalized for a tournament with any number of teams.
The key observation is that after each match, one team is eliminated. Therefore, to determine the champion of a n competing teams, n-1 teams must be eliminated, meaning there must be n-1 matches played. So the answer to the problem above is 65 matches.