Single Elimination Practice - Scheduling

You are in charge of programming a 3-on-3 basketball tournament as part of World Sports Day at SDSU.  The participants will represent some of the countries that have students at attending SDSU.  You are going to play games at the HPER, using 2 courts for 4 hours per day (5pm, 6pm, 7pm, and 8pm).  You will begin games on Saturday, November 4 and play games every day through Wednesday, November 8 (5 days).  You are allowing 1 hour for each match scheduled, and participants MAY only play one match per day.

1.  Figure out the number of entries you can accommodate in your tournament.

2.  Draw the single elimination bracket for the number of entries in your tournament.

3.  Seed the entries, and indicate their positions with the numbers 1, 2, 3 ....

4.  Position byes appropriately.

5.  Schedule the matches.  List day, date, court and time of matches.

6.  Determine how much money will be spent for officials if you provide 2 per court per match at $10 per official per game.

Single Elimination Practice - Forecasting Number of Days

1.  N=45 teams
    Number of games that can be played each day: 3

2.  N=87 teams
    Number of games that can be played each day: 9

3.  N=27 teams
    Number of games that can be played each day: 5

4.  N=36 teams
    Number of games that can be played each day: 6

5.  N=64 teams
    Number of games that can be played each day: 7

Here's a word problem:

You are the intramural coordinator for XYZ University.  Your director has asked you to determine the number of days it will take to play your intramural basketball playoffs, consisting of 38 teams.  You have the facility reserved Monday through Thursday and you are able to play 6 games per day.

 Single Elimination Practice - Index Numbers/Minimum Number of Games

1.  N=48 teams
    Number of days that are available: 10

2.  N=37 teams
    Number of days that are available: 13

3.  N=24 teams
    Number of days that are available:  5

4.  N=20
    Number of days that are available: 4

5.  N=64 teams
    Number of days that are available: 10

Here's a word problem:

You are programming a youth ice hockey tournament in order to help the new professional ice hockey expansion team (the Brooking Bulldogs) build community support for their franchise.  The Bulldogs are allowing you to utilize their practice facility to play your single elimination tournament.  You have 22 teams signed up to play and the Bulldogs have allowed you to play for 4 days in their building.  What is the minimum number of games that you must be able to play per day in order to complete your tournament in 4 days?

 Single Elimination Practice - Wasted Games/Minimum Number of Entries

Under the conditions below, find the minimum number of entries the single elimination tournament can handle.  Assume no team is playing more than ONCE per day:
 

1.  Number of games that can be played per day: 4
    Number of days that are available: 8

2.  Number of games that can be played per day: 10
    Number of days that are available: 10

3.  Number of games that can be played per day: 7
    Number of days that are available:  7

4.  Number of games that can be played per day: 5
    Number of days that are available: 16

5.  Number of games that can be played per day: 16
    Number of days that are available: 7

Here's a word problem:

You did such a good job with the youth ice hockey tournament that the Bulldogs have hired you on their staff as a community services coordinator!  As such, you are responsible for programming an adult ice hockey tournament to achieve the same goals as your youth tournament.  Unfortunately, the Bulldogs are now in training camp, and the facilities that they have made available to you are pretty restricted.  They have allowed you to play 4 games per day for a total of 7 days in their practice facility.  You have a huge interest in the tournament from the adults in the community.  How many teams can you enter into the tournament?

You have the opportunity to design a single elimination tournament for your HS basketball team. This will serve as a fundraiser for your team. You have seventeen entries and the ability to play 9 games each day. What is the minimum number of days you will need to conduct this single elimination tournament?