1. Problem Set 2 Problem #6 By: Zac Snively

2. Question Presented  In a league that has 6 teams, every team plays every one of the other teams twice in a season. What is the total number of games played in a season?

3. Setting up the problem  For the sake of the problem I will name the six teams in the league A,B,C, D, E, F.  Each team has to play every team twice.  So each team will play a total of ten games in a season

4. Schedule Week 1 A vs. B C vs. D E vs. F Week 2 B vs. C D vs. E F vs. A Week 3 B vs. E D vs. F A vs. C Week 4 A vs. E D vs. B C vs. F Week 5 E vs. C F vs. B D vs. A

5. Through the five weeks  Each week there are 3 games.  In five weeks there have been a total of 15 games.  Everyone has played each other one time

6. Where are we now?  Each team has played every other team in the league once.  The question however states that they must play everyone in the league twice.  So we need to double the amount of games that we currently have.

7. The answer  So for everyone in the league to play each other team two times there will need to be a total of 30 games played for the season.