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My boss is hosting a formal networking event where there are a total of 49 participants. There are 7 tables and 7 people at each table. The idea is for each participant to meet every other participant without meeting the same people again - if this is not possible, then to minimize meeting up with the same people. After round one - some participants move to other tables, after round two - , etc., etc.

Submitted: 457 days and 14 hours ago.
Category: Math
Value: $30
Status: AWAITING EXPERT REPLY
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Accepted Answer

Thanks, XXXXXXXXXXX, for using Just Answer.

Assuming that everyone at the same table is presumed to have met each other, the answer is that it can be done, but the simplest explanation of how to do it involves arithmetic modulo 7.

Number each person of the 49 persons with 2 numbers x and y between 0 and 6 (inclusive), such that no two persons have the same pair of numbers. Number the tables 0 to 6, as well.

For the first round, let each person sit at the table corresponding to the second number y.

For the second round, let each person sit at the table corresponding the their first number x.

For the third round, let each person sit at the table corresponding to the (x+y) modulo 7.

For rounds n from 4 to 8, let each person sit at the table corresponding to x + (n-2) y, modulo 7.

I don't know the level of mathematics you are allowed to use, but this works because the numbers 0-6 module 7 form a field.

Picture
Expert: Dr. Arthur Rubin
Pos. Feedback: 100.0 %
Accepts: 101
Answered: 12/16/2008

Mathematician

Ph.D. in Mathematics, 1978, from the California Institute of Technology, over 20 published papers

457 days and 14 hours ago.

Reply

Dr. Rubin: WOW! Thanks so much for your fast response. I have to leave the office for an appointment and don't have any time right now to think about your answer. I think I know what you mean, but I may have a question. Will get back with you tomorrow morning. THANKS!!!

455 days and 21 hours ago.

Reply

Dr. Rubin:

 

For an additional fee would you be willing to make an x, y chart for me showing something like this: x = tables 0-6, y = rounds 0-6 and the numbers in the boxes = players 0-48 (or however it makes most since to put together)?

 

The bottom line is I would like give each play a card that shows their Player Number and what Table they sit at for each Round. From such a chart, I think I would be able to easily gather this information.

 

Look forward to hearing from you.

 

Many thanks for your answer - IT'S POSSIBLE!

Crystal

 

 

Posted by Dr. Arthur Rubin 455 days and 17 hours ago.

Info Request

I should be able to produce a spreadsheet with the numbers by this evening (Pacific Time), with formulas describing how the table number in each round is calculated. It may take a little work, though.

Probable format:

Column 1: player number
Columns 2-3 or 4: intermediate calculations
Columns 5-12: table number for rounds 1-8.

Would this be acceptable?

455 days and 16 hours ago.

Reply

Dr. Rubin: I think so - as long as I can tell from this where people need to be that works for me!

 

Looking forward to how this works.

 

Thanks so much,

Crysatl

Accepted Answer

OK, here it is.

 

Player numbers are 0 to 48 in the first column (A), and the table numbers (0 to 6) for each of the 8 rounds are in the indicated columns (E through L)

Picture
Expert: Dr. Arthur Rubin
Pos. Feedback: 100.0 %
Accepts: 101
Answered: 12/18/2008

Mathematician

Ph.D. in Mathematics, 1978, from the California Institute of Technology, over 20 published papers

455 days and 14 hours ago.

Reply

Dr. Rubin: Wow - this is amazing. I can work with this. I'm going to make the player cards. We'll see how it works on 01-14-09 - that's the date of the formal networking event. I'm sure it will work perfect, but I'll follow up with you after the event and let you know if I did it right.

 

Many Thanks!

Crystal

Posted by Dr. Arthur Rubin 455 days and 14 hours ago.

Info Request

Dear Crystal,

 

Did you intend to Accept a second time? I don't mind having the additional money, but you really didn't need to do that.

Dr. Arthur Rubin39800.7951683218

455 days and 14 hours ago.

Reply

Yes, I did - You're worth it!

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