Hi everyone,

I am a junior high teacher and I'm working on creating a schedule for field day for the kids this year. I have been struggling over a schedule that works for our situation and I'm starting to think that the ideal schedule isn't possible due to all the requirements. Here's what I need, and how I've been tackling it:

-12 teams, arbitrarily named A-L
-12 events (havent thought of them all yet but don't worry about it)
-12 "sessions" on the schedule
-Every team must play every other team at least once (one will be repeated)
-Every team must play every event exactly once
-Every team must have something to do during all sessions, and can't be scheduled for two things at once

It would be no problem at all if each team didn't have to play every other team, or if each team didn't have to play every other event. However, every method I've tried has ended up with a huge roadblock about halfway through. I even had a bunch of the students trying to work on it too since it ends up being a bit like a giant sudoku puzzle, but they weren't able to crack it either.

I got pretty concerned when I tried to break it down and create a similar shcedule with the same requirements but with only 4 teams - and couldn't do it. I didn't spend too long on that though so I may have missed something obvious.


My method: I made a 12x12 grid, and made 66 little cards with each combination of teams (AB, AC, AD, etc). Columns of the grid represent the time slots, rows of the grid represent the events. Every row needs to have every letter appear exactly once, and every column needs each letter to appear exactly once. Empty spaces on the grid are fine, each event chaperone would get a break during those sessions. And for their final event, each team would have to repeat playing against one of their previous opponents, but thats fine too.

Is there a better way to do this? I tried using a few round-robin schedule generators and read a few excel tutorials but none of them had all the requirements covered. I would appreciate any help you can offer on this.

Thanks,
HBE

I don't think this is possible. It looks like you have too many restrictions.

I think the problem is that you can only run 6 events at a time. You have a lot of "wasted" space on those events when they're empty, and that is a severe limitation to your flexibility in assigning the activities.

You might want to scale back to 9-10 events and try again. This sounds like it's a big enough thing that it might be good to take a couple water breaks throughout the day. (15 minutes/event * 12 events = 3 hours)

Doing so will also buy you some buffers for when some games run overtime (which is very likely to happen).

Are all the games necessary to run as head-to-head matchups? Can you create some sort of point system instead?

This is a Classical Algebra problem and requires modulos.
You guessed correctly; it is impossible for this reason:

"Every team must have something to do during all sessions, and can't be scheduled for two things at once"

Thanks everyone for your input. I think its more fun with teams going head-to-head on each event, but I did plan on giving points for each event based on performance relative to all teams, not just your direct opponent. I'm going to look over responses from OOT, here, and POG and see what works best.

I appreciate your help,
HBE