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#1 2012-12-14 06:28:46

tlc1971
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Christmas gift rotation

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.

#2 2012-12-14 07:56:41

bobbym
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Re: Christmas gift rotation

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#3 2012-12-17 09:29:58

John E. Franklin
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Re: Christmas gift rotation

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

#4 2012-12-24 15:35:54

tlc1971
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Re: Christmas gift rotation

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?

#5 2012-12-24 21:47:33

bobbym
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Re: Christmas gift rotation

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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