It's that time of year again, March Madness. You cannot look at the news without seeing the results of a high school or college basketball tournament. This activity will help familiarize you with some of concepts of the tournament structure. First, we will look at setting up a tournament:

1. You are in charge of setting up a high school tournament involving 8 teams. You have their regular season records and can rank them from first through 8th place. Your team finished in 3rd place, and you want to find out who you will play in the tournament. A tree diagram is helpful in finding this information. Set up the tree in this manner:

a) If all goes as planned, who should win the tournament ? Label the vertex at the top of the tree with this team number.

b) Draw the first two branches of the tree. The two new vertices represent the teams in the finals. Barring upset, which two teams should this be? Label these vertices with these team numbers.

c) Now construct the next 4 branches of the tree. What do these four new vertices represent? As before, label the team numbers as you see fair.

d) Continue this process until all eight teams are assigned vertices. As the 3rd place team, who would you play in the first round?

2. Since each game involves exactly two teams, what type of tree will this be ? Also, describe what the root and leafs of this tree represent.

3. Suppose that only 7 of the eight teams will compete in the tournament. Describe a fair method to take care of this situation.

4. The concept of a bye is important to tournament bracketing. This year, the University of Colorado is competing in the Big 12 conference. (Up from the Big 8) Create a tree to represent a twelve team tournament. How many teams will get byes in the first round?

5. How do tournament trees and tournament brackets differ?

6. It is important for the tournament host to know how many total games must be scheduled to run a tournament with 8 teams? with 12 teams? with 32 teams? 256 teams?

7. Complete the following table:

# of teams	# of rounds	total # of	# of teams	# of rounds	total # of
competing	necessary	games needed	competing	necessary	games needed
4	_________	___________	32	_________	___________
8	_________	___________	64	_________	___________
12	_________	___________	128	_________	___________
16	_________	___________	N	_________	___________

8. What generalizations can you make about a tournament with "N" teams ?