NCAA Basketball Tournament - Bracketology

The National Collegiate Athletic Association (NCAA) is a single elimination tournament. If a team loses a game they are out of the tournament. Over the years, the NCAA basketball tournament has grown from a field of 8 teams to 64 teams to currently 68 teams. There is pressure for the NCAA to expand the tournament to include even more teams.

  1. Investigate the tournament design and create a function that will determine the number of games the champion will need to win, given any number of teams in the tournament.
  2. How will adding teams to the tournament affect the number of games the champion must play? Is it always equal for every team? Explain.
  3. Consider the following history chart of the NCAA Men's Basketball Tournament. Determine the minimum number of games each champion played.
  4.                  Year Number of Teams Minimum Games Played by Champion Total Number of Games Played
    1940 8
    1952 16
    1956 25
    1975 32
    1979 40
    1980 48
    1984 52
    1990 64
    2011 68
  5. How many more teams must be added to the current tournament schedule in order to guarantee the next champion has to play one more game than they do currently? Explain.
  6. What is the total number of games that need to be played each year?