Quandaries and Queries

I saw that someone put on your web site a team schedule and you helped them figure it out.  I have 6 teams that want to play each other once, and believe it or not, I cannot figure it out.  Any help?

Hi,

The number of ways of choosing 2 teams from 6 teams is 6-choose-2 which is 15.Thus you need 15 games if each team is to play each other team. On any one day you can have at most 3 games and hence you will need at least a 5 day schedule. Here is one way to construct a schedule.

Label the teams 1, 2, 3, 4, 5 and 6. On each day team 1 plays one of the other teams so we can start as follows.

 Day 1 1-2 Day 2 1-3 Day 3 1-4 Day 4 1-5 Day 5 1-6

Now consider team 2. On day 2, team 2 could play team 4, on day 3 team 5 and on day 4 team 6. The only team left for team 2 to play is team 3 so they can play on day 5.

 Day 1 1-2 Day 2 1-3 2-4 Day 3 1-4 2-5 Day 4 1-5 2-6 Day 5 1-6 2-3

The remaining games on days 2, 3, 4 and 5 are determined at this point.

 Day 1 1-2 Day 2 1-3 2-4 5-6 Day 3 1-4 2-5 3-6 Day 4 1-5 2-6 3-4 Day 5 1-6 2-3 4-5

If you look at the list so far you will see that the matches that arre missing are 3-5 and 4-6 an thus the schedule is completed by having these games on day 1.

 Day 1 1-2 3-5 4-6 Day 2 1-3 2-4 5-6 Day 3 1-4 2-5 3-6 Day 4 1-5 2-6 3-4 Day 5 1-6 2-3 4-5

Penny

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