Quandaries and Queries


I have to make a schedule for my fantasy football league. There are 10 teams in the league and we play a 13 week season. The challenge is we want to play each team only once during the first 10 weeks. This way no team will play another team twice without having played each team at least once. Is this possible?


Hi Jim

I am going to use a technique I used before in a golf schedule.

Draw a circle, space the digits from 1 to 9 around the circumference and place the integer 10 at the center. Draw lines connecting pairs of integers as in the diagram below.

This gives the games for week 1.

1-10, 2-9, 3-8, 4-7, and 5-6.

Now rotate the digits counterclockwise around the circumference.

This gives the games for week 2.

2-10, 3-1, 4-9, 5-8, and 6-7.

Rotate the digits counterclockwise around the circumference again to get the games for week 3. After 9 weeks you will have each team playing each other team exactly once and you have 4 weeks left to complete the season.



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