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#1 2012-12-13 07:28:46

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

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.

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#2 2012-12-13 08:56:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 92,282

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#3 2012-12-16 10:29:58

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,585

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

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#4 2012-12-23 16:35:54

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

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?

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#5 2012-12-23 22:47:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 92,282

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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