Progressive Dinner

KarenL · 2009-06-26 00:02:41

I am trying to plan a progressive dinner with 16 couples. We have planned 5 courses so that every couple will get to eat once with each other couple. There will be 4 homes hosting each of the 5 courses. There will obviously have to be 4 couples hosting twice. Can anyone help me with a chart?

bobbym · 2009-07-04 08:08:33

Hi KarenL;

You can have 5 courses like this. It's the same as before for the first 4 courses.

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

Course 5

host= 1 3 4 2
host= 5 7 8 6
host= 9 11 12 10
host= 13 15 16 14

Peter3j · 2011-08-15 14:26:26

How about a progressive dinner for 36 (16 men/16 women), 6 people/table (4 tables), 4 courses?

Thanks!

bobbym · 2011-08-15 14:34:14

Hi Peter3j;

16 men and 16 women is only 32 people. What are the other positions going to be?

peter3j · 2011-08-16 01:25:52

Hi bobbym - Thanks for the reply!

I can't seem to count or type these days! Yes, 16+16 is 32, not 36!

The problem is for 36 people (18 men, 18 women), 6 per table (*6* tables), 4 courses.

(The actual number of the dinner being planned is 40 - but I doubt that would be workable...?)

Wish there wre a generalizable algorithm for this.

Thanks again - Peter

bobbym · 2011-08-16 01:42:38

Hi;

It is known that the problem you are asking is equivalent to finding a pair of 6 by 6 orthogonal squares. It is also known that such a thing is impossible. So a 4 course progressive dinner of 6 tables with 6 seats is impossible. You will have to try another arrangement.

A 3 course is possible.

peter3j · 2011-08-16 02:34:43

Hey bobbym - Thanks for the quick response - Much appreciated!

I had suspected that there might not be a solution to this arrangement.

Could you post the 3-course solution? A friend is hosting a 36-person progressive
dinner, and even a 3-course seating plan would be helpful!

Thanks again - Peter3j

bobbym · 2011-08-16 03:01:52

Hi;

Label your people 1 - 36 and enjoy your dinner! Do not forget to save me some!

Each row across is one course.

Peter3j · 2011-08-16 03:32:29

Wow! Thanks so much - do you want the salmon or the steak?

This is great - I'm not sure that this keeps 3 man/3 women at each table (?) - that might make the
problem even more insolvable.

Peter

bobbym · 2011-08-16 03:48:38

Hi;

You did not mention that in your question. This seating will definitely
not do that.

Maybe we could keep pairs together?

Peter3j · 2011-08-16 04:00:21

Hi bobbym,

My bad - I did not make it clear that this is a singles dinner (not the usual couples dinner) and that
the idea is to keep 3 men and 3 women at each table, allowing each man to sit at a table with
different women each course (and vice-versa for women) so that he/she gets to sit with
as many she/he as possible - hopefully each man/woman will be able to sit with every woman/man.

At past dinners the 3 men have shifted tables at each course, but we've never been able to get
to the point where every man has sat with every woman, and every woman has sat with every man.

Again, this might not be possible (?). Or there may be numbers (32 total, 38 total, etc) for which it is
possible - using different numbers at each table, different number of tables, etc, as long as there is
gender parity at each table.

Peter

bobbym · 2011-08-16 04:11:38

Hi;

In the above table each man will get to sit with 6 different women.
The maximum amount is of course 9 different women. Each table can have
3 women, so obviously 3 * 3 = 9 is the maximum possible.

Jason1973 · 2011-09-02 15:08:32

Hi!!

I am planning a progressive dinner for approximately 50 people, but it may go up to as many as 100. We will be having a 3 course meal, each course served at a different house. Can you give me a slab breakdown for 50, 75, 100? or any numbers that would wrk in that range? Thank you sooo much!!

Jason Leonardo
Everything Expats
Pune, India

Jason1973 · 2011-09-02 15:35:33

Sorry, forgot to mention that we will have 10 people per table at this event.

Jason
Everything Expats
Pune, India

bobbym · 2011-09-02 16:57:30

Hi Jason;

This is a very difficult problem. I have had some luck with them in the past here
but please keep in mind that there are no answers for most arrangements.
Please be a little more specific on how many and whom is going to sit
together.

Apollo13 · 2012-05-02 11:46:37

Hi,

Hoping you can help me.

I am running a networking event for 112 people and have 14 tables of 8. Do you have a formula so each person rotates around the room and meets each person once?

bobbym · 2012-05-02 11:49:06

Hi Apollo13;

There is no formula, they are run off by computer which will produce a chart. Also not every seating arrangement has a known solution.

Math Is Fun Forum

#1 2009-06-26 00:02:41

Progressive Dinner

#2 2009-07-04 08:08:33

Re: Progressive Dinner

#3 2011-08-15 14:26:26

Re: Progressive Dinner

#4 2011-08-15 14:34:14

Re: Progressive Dinner

#5 2011-08-16 01:25:52

Re: Progressive Dinner

#6 2011-08-16 01:42:38

Re: Progressive Dinner

#7 2011-08-16 02:34:43

Re: Progressive Dinner

#8 2011-08-16 03:01:52

Re: Progressive Dinner

#9 2011-08-16 03:32:29

Re: Progressive Dinner

#10 2011-08-16 03:48:38

Re: Progressive Dinner

#11 2011-08-16 04:00:21

Re: Progressive Dinner

#12 2011-08-16 04:11:38

Re: Progressive Dinner

#13 2011-09-02 15:08:32

Re: Progressive Dinner

#14 2011-09-02 15:35:33

Re: Progressive Dinner

#15 2011-09-02 16:57:30

Re: Progressive Dinner

#16 2012-05-02 11:46:37

Re: Progressive Dinner

#17 2012-05-02 11:49:06

Re: Progressive Dinner

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