[Math] Scheduling a team based activity with 10 different teams and X different games. Every team must meet each other ONCE but never twice,

Question

Hi there I am planning a ”Scavenger hunt”-like activity (I have no other words for this event), and I am having trouble creating the schedule.

The idea of this hunt/run/game/competition is that 10 teams will battle each other at X different mini games. The games on are team vs. team based, meaning that there will always be two teams on each post and one winner and one loser.

I require that every team fights every other team. Meaning that team 1 will have to meet team 2, 3, 4, 5, 6, 7, 8, 9, and 10, and team 2 will have to meet team 1, 3, 4, 5, 6, 7, 8, 9, 10 (and so forth). The amount of mini games must be so, that every team only meets the other teams ONCE each, but still they have to meet every team.

How many posts do I need to create, and how could I schedule the overall activity? (A table of rounds and teams would be much appreciated).

Answer 1

• Here is a proposed schedule with 9 rounds of 5 matches each: http://tournamentscheduler.net/schedule/NjkwMTM0ODg2
• This is the best possible since you need $10\times 9/2=45$ matches and you can have at most 5 matches per round.
• Here is a lovely explanation of how to construct such "round robin" tournaments: http://nrich.maths.org/1443
• Here is the tool used for the above schedule: http://tournamentscheduler.net/