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#1 2009-06-26 02:16:04
- KarenL
- Member
- Registered: 2009-06-25
- Posts: 3
Another progressive dinner
I wish to plan a progressive dinner with 16 couples. If we have 4 courses and 4 hosts for each course, how can I plan a chart for where no one eats together twice?
Each couple would eat with 12 other couples.
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#2 2009-06-26 12:53:14
- John E. Franklin
- Member
- Registered: 2005-08-29
- Posts: 3,588
Re: Another progressive dinner
Course #1:
Host 0 and 4 8 C
Host 1 and 5 9 D
Host 2 and 6 A E
Host 3 and 7 B F
Course #2:
Host 4 and 1 A F
Host 5 and 2 B C
Host 6 and 3 8 D
Host 7 and 0 9 E
Course #3:
Host 8 and 3 5 E
Host 9 and 0 6 F
Host A and 1 7 C
Host B and 2 4 D
Course #4:
Host C and 3 6 9
Host D and 0 7 A
Host E and 1 4 B
Host F and 2 5 8
igloo myrtilles fourmis
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#3 2009-06-26 13:11:37
- mathsyperson
- Moderator
- Registered: 2005-06-22
- Posts: 4,900
Re: Another progressive dinner
Course #1:
Host 0 and 4 8 C
Host 1 and 5 9 D
Host 2 and 6 A E
Host 3 and 7 B F
Course #2:
Host 4 and 1 A F
Host 5 and 2 B C
Host 6 and 3 8 D
Host 7 and 0 9 E
Course #3:
Host 8 and 3 5 E
Host 9 and 0 6 F
Host A and 1 7 C
Host B and 2 4 D
Course #4:
Host C and 3 6 9
Host D and 0 7 A
Host E and 1 4 B
Host F and 2 5 8
Couple 0 eats with 7 and 9 twice in that arrangement.
I didn't check any others.
Why did the vector cross the road?
It wanted to be normal.
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#4 2009-06-27 02:48:51
- Ricky
- Moderator
- Registered: 2005-12-04
- Posts: 3,791
Re: Another progressive dinner
I wish to plan a progressive dinner with 16 couples. If we have 4 courses and 4 hosts for each course, how can I plan a chart for where no one eats together twice?
Each couple would eat with 12 other couples.
What kind of math class are you in? Have you ever heard of a balanced incomplete block design?
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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#5 2009-06-27 05:39:24
- John E. Franklin
- Member
- Registered: 2005-08-29
- Posts: 3,588
Re: Another progressive dinner
Oops! I guess I didn't check my work, sorry.
I've also found more errors.
These pairs are duplicated:
6-3 0-9 0-7 8-3 8-5 A-1 A-7 B-2 1-4 4-B
So it's a long way from perfect, sorry.
igloo myrtilles fourmis
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#6 2009-06-30 12:35:42
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Another progressive dinner
Hi KarenL;
If you number the people 1 to 16. Then they can eat in this manner with the hosts being the first column.
Course 1
host= 1 5 9 13
host= 2 6 10 14
host= 3 7 11 15
host= 4 8 12 16
Course 2
host= 5 12 15 2
host= 6 1 11 16
host= 7 4 10 13
host= 8 9 14 3
Course 3
host= 9 15 4 6
host= 10 5 3 16
host= 11 13 8 2
host= 12 14 1 7
Course 4
host= 13 12 6 3
host= 14 11 5 4
host= 15 10 8 1
host= 16 9 7 2
Last edited by bobbym (2009-06-30 12:37:24)
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.
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#7 2009-06-30 16:29:13
- KarenL
- Member
- Registered: 2009-06-25
- Posts: 3
Re: Another progressive dinner
BobbyM,
You must be a genius!! Thanks so much for figuring this out for us!!
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#8 2009-06-30 17:45:43
- MathsIsFun
- Administrator
- Registered: 2005-01-21
- Posts: 7,711
Re: Another progressive dinner
Bobby: could this be automated? "Progressive Dinner Tool" ... ?
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
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#9 2009-06-30 23:02:32
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Another progressive dinner
Hi MathsisFun;
I can't say at this time. Although it took a lot of computer help, it also took a lot of human trial and error. In other words I don't yet have an algorithm. I am going to work on her other problem and maybe see if it can be automated.
Hi KarenL;
Nothing even approaching genius, just a lot of hard work. A genius told me that I was bad at math, chess, computers and german. See post #23 of the link below.
http://www.mathisfunforum.com/viewtopic.php?id=10993
That's proof enough for me.
Last edited by bobbym (2009-07-01 00:07:58)
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.
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#10 2009-07-04 11:20:17
- MathsIsFun
- Administrator
- Registered: 2005-01-21
- Posts: 7,711
Re: Another progressive dinner
A genius told me that I was bad at math, chess, computers and german.
Are you referring to the genius who can't use the "quote" tags? 
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
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#11 2009-07-04 11:37:18
- mathsyperson
- Moderator
- Registered: 2005-06-22
- Posts: 4,900
Re: Another progressive dinner
For some reason that made me wonder, if "ARB" was an onomatopoeic word, what sound would it describe?
I'm thinking a dog barking through a wall.
(Karen, feel free to steer us back on topic whenever you like. 
)
Why did the vector cross the road?
It wanted to be normal.
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#12 2009-07-04 12:19:30
- MathsIsFun
- Administrator
- Registered: 2005-01-21
- Posts: 7,711
Re: Another progressive dinner
Dog barking through a wall! Perfection!
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
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#13 2009-07-04 19:53:18
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Another progressive dinner
Hi Mathsisfun;
Yes, his username says it all. He is a math genius.
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.
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