The NCAA Basketball Tournament is a single elimination tournament in each of four regions. 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.
First we will investigate one single elimination tournament.
1.
Investigate single elimination 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 does 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 chart of some single elimination tournaments based on the number of teams. Determine the minimum number of games each champion played.
Number of
Teams
8
16
25
32
40
48
52
64
68
Minimum Games Played by
Champion
Total Number of Games
Played
NCAA 1

4.
Bracketology is the process of predicting the field of the NCAA Basketball Tournament , named as such because it is commonly used to fill in tournament brackets for the postseason.
Assume your teams are: A, B, C, D, E, F, G, H, (or give them some other names) and fill in your bracket:
NCAA
How many ways are there to fill in your bracket?
If you filled in your bracket randomly, what is the probability that you bracket will match the outcome of the tournament?
How many ways are there to fill in your bracket for some of the tournaments listed in the chart in problem number 3?
In particular, how many ways are there to fill in the brackets for a tournament with 64 teams?
It was reported that
“Combinatorics calculates that randomly picking the outcomes of every game in the NCAA tournament stands one chance of success in more than
18 quintillion. If every person on Earth could fill out a bracket every second, then it would take them roughly one century to fill out all possibilities.”
Can this quote possibly be true? (Explain using a 64 team single elimination tournament.) reference: http://www.sciencedaily.com/videos/2006/0301betting_on_march_madness.htm
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