Math Is Fun Forum

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Christmas gift rotation

Hi tlc1971;

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

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

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??

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igloo myrtilles fourmis

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?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.