1. Designing Tournaments
Colby Nadeau, Gus Johnson, and Taylor Gagne
Mentor: Professor Dinitz

2. Types of Tournaments Elimination Round Robin Consolation
Single Elimination
Double Elimination
Round Robin
Consolation
Ladder Tournaments

3. Elimination Trick
How many games are played in a single elimination tournament with 64 competitors?
63 games
How many games are played in a single elimination tournament with 12 competitors?
11 games
How many games are played in a single elimination tournament with 973 competitors?
972 games

4. Round Robin Tournament
A round robin tournament is a competition where every competitor plays against every other competitor one time.
Real World Examples:
FIFA World Cup Qualifier
World Chess Championships
Cricket World Cup

5. Round Robin (2n) Games Per Week = 2n/2 Weeks = 2n-1
If 2n = 2 then there is only 1 game
1 plays 2 shown as (12)
If 2n = 4 then there are 2 games a week for 3 weeks
Week #1 = (12) (34)
Week #2 = (13) (24)
Week #3 = (14) (23)

6. 2n = 6 There are 3 games a week for 5 weeks
There is a much easier way to do this!

7. Starter Construction
If 2n = 10 then there are 5 games a week for 9 weeks 8 5 7 6 4 2 3 1 ∞
Week 0 0∞ 45 81 36 72
Week 1 1∞ 56 02 47 83
Week 2 2∞ 67 13 58 04
Week 3 3∞ 78 24 60 15
Week 4 4∞ 80 35 71 26
Week 5 5∞ 01 46 82 37
Week 6 6∞ 12 57 03 48
Week 7 7∞ 23 68 14 50
Week 8 8∞ 34 70 25 61

8. Number of Variations vs. Players
There are different variations to how you could set up these tournaments depending on how many contestants there are.
Professor Dinitz helped discover that there are different round robin tournament with 12 players.
Number of Players 2 4 6 8 10 12
Number of Variations 1
396

9. References/Thanks References
Professor Dinitz
We want to thank Professor Dinitz for helping us learn and prepare for our presentation.