[NA] Need Help Making 6 Groups of 13 ...

[Erice]

I am supposed to come up with six sets of three groups of 13 people so that each person is with each of the 38 other people on the list in at least one of those sets. Basically, this is a campout where I have 39 kids coming, and we have six different activities. There will be 3 groups of 13. I want to make sure each kid can be with every other kid in at least one of those activities.

Is there an algorithm that can help make this happen? I have used Excel, given each kid a random number, then sorted the column of random numbers to shuffle the names into groups. But making sure each kid is with every other kid at least once is the hard part. I end up moving kids by hand from one list to the other, but eventually I end up moving someone who "worked" to accommodate one person, only to find out when I complete the list, that my moving made it not work again.

It is kind of hard to explain ...

I wonder how flight dispatchers and/or crew schedulers do it ???!

There must be a way to leverage technology to help me with this. Any suggestions would be appreciated.

 

[SixPapaCharlie]

flashbacks to programming homework

 

[Erice]

flashbacks to programming homework

I KNEW I should have paid more attention in that class!

Most of what I am finding is about Combinations (nCr) and how to tell HOW MANY different groups I can make. I don't care about that--I just want to know how to make ONE that works!

 

[cgrab]

So you have 18 events, that is 3 groups each doing 6 things. You have 39 factorial combinations of students. It can not be done.

A good option is to have 39 cards with 13 sets of 1 through 6 printed on them. Each set of cards starts with a new number like a shotgun start in golf. Have the kids pick the cards at random and then make it a quest but try not to let them think of it as a class schedule.
The random ness will mix the kids but they will be together in their group the whole weekend.

 

[murphey]

Additional criteria question - will everyone participate in each activity?

 

[Erice]

Additional criteria question - will everyone participate in each activity?

Yes, everyone participates in each activity.

So you have 18 events, that is 3 groups each doing 6 things. You have 39 factorial combinations of students. It can not be done.

I think I understand the factorial concept. I am looking for combinations of 39 things taken 13 at a time. 39C13 gives 39!/((13!)(26!)), which is over 8 billion combinations. But making sure there is a 1-to-38 in at least one in the six groups seems to be where it breaks down.

I just want to know what the magic size and number of groups would be in order to make this work.

A good option is to have 39 cards with 13 sets of 1 through 6 printed on them. Each set of cards starts with a new number like a shotgun start in golf. Have the kids pick the cards at random and then make it a quest but try not to let them think of it as a class schedule.
The random ness will mix the kids but they will be together in their group the whole weekend.

Well, I want to change the groups for each activity. And maybe making six random groups is the best I can do...

 

[Cpt_Kirk]

Just have one big game of dodgeball.

Nothing helps remind you of your place in the world like dodgeball.

 

[Sac Arrow]

I think Karl Marx worked out that social algorithm a long time ago.