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**tlc1971****Member**- Registered: 2012-12-13
- Posts: 2

Our family gives gifts to only 2 members at a time. We want to have a rotation that allows 3 families to give to each other at a time so they can visit and exchange gifts. There are 11 members- how can we do this? I started simply with 123 give to each other, 456, then 789 and then just 2 families 10 and 11. I want the combinations to work so that each family gives to all the other families with as few repeats as possible so the next combo might 1 4 10, 2 5 11, 3 6 9, 5 and 8. Please help with a formula that would work.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,237

Hi tlc1971;

Welcome to the forum. I am having trouble with your question. Could you explain a little better?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,562

does this work for your holiday??

1 gives to 4 and 8.

2 gives to 5 and 9.

3 gives to 6 and A.

4 gives to 7 and B.

5 gives to 8 and 1.

6 gives to 9 and 2.

7 gives to A and 3.

8 gives to B and 4.

9 gives to 1 and 5.

A gives to 2 and 6.

B gives to 3 and 7.

How's dat??

**igloo** **myrtilles** **fourmis**

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**tlc1971****Member**- Registered: 2012-12-13
- Posts: 2

Let me explain better.

We want a gift rotation that can be easily changed year to year. Currently it works like John Franklin's suggestion. However we want something more complex.

We would like to have groups of 2 or 3 families visit each other and give gifts. Since there are 10 siblings, and 1 parent group, we will actually have 3 families, 3 families, 3 families, and 2 families. So year 1 would look like this: Families are numbered 1-11 and each line represents a group who would visit and exchange gifts

1,2,3

4,5,6

7,8,9

10,11

So then in year 2 we don't want anyone visiting the same people- it might look like this

1,4,7

10,2,5

8,11,3

6,9

So, then it gets complicated to keep people visiting different people each year. I want to optimize and make this work. My husband suggests doing it like a partial n chart- Any thoughts how to make it so everyone visits everyone else in the fewest number of years possible?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,237

Hi;

Thanks for the better explanation. There are solutions but only for 4 years.

Each row represents a year. You were correct for the first two years.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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