# Need help! :) "3 couples at dinner" puzzle

• Oct 11th 2012, 06:27 AM
financestudent86
Need help! :) "3 couples at dinner" puzzle
Hi. I have a math problem and wonder if anyone can help me solve it and perhaps explain how. The problem is:

3 couples, all consisting of man & woman, eat dinner together at a gathering. The man in couple A (which I have denoted as A subscript 1) knows everyone at the gathering. Q is; Who does his wife (A subscript 2) know?

I have posted a suggestion for a start of how it supposedly can be solved. I have denoted "0" as "no new acquaintance" so an idea is to use "1" as "new acquaintance". I hope someone can help.. Thanks!

• Oct 26th 2012, 03:15 PM
HallsofIvy
Re: Need help! :) "3 couples at dinner" puzzle
This makes no sense. There is no reason given to think that who the husband knows has anything to do with who his wife knows. Surely there is some other information like "if one member of a couple knows a member of another couple, his partner must know at least one person in the other couple"?
• Oct 29th 2012, 08:03 AM
Soroban
Re: Need help! :) "3 couples at dinner" puzzle
Hello, financestudent86!

I agree with HallsofIvy; the problem makes no sense.

Quote:

Three couples, each consisting of man & woman, eat dinner together at a gathering.
The man in couple A (which I have denoted as A-sub-1) knows everyone at the gathering.
Who does his wife (A-sub-2) know?

I have posted a suggestion for a start of how it supposedly can be solved.
I have denoted "0" as "no new acquaintance" so an idea is to use "1" as "new acquaintance".
I hope someone can help. .Thanks!

Is the relationship "knows" symmetric?
That is, if $A_1$ knows $A_2$, can we assume that $A_2$ knows $A_1$ ?

Your "picture" needs some explaining, too.

If that is a Seating Chart, it seems that couple-A sits at the first table,
. . couple-B sits at the second table, couple-C sits at the third table.
I don't see how the seating affects the friendshps.

If it is an Elimination Table, it should be 6-by-6
. . with no 2-by-2 subsets indicated.

. . $\begin{array}{c||c|c|c|c|c|c|} & A_1 & A_2 & B_1 & B_2 & C_1 & C_2 \\ \hline \hline A_1 & \times & 1 & 1 & 1 & 1 & 1 \\ \hline A_2 & & \times &&&& \\ \hline B_1 &&& \times &&& \\ \hline B_2 &&&& \times && \\ \hline C_1 &&&&& \times & \\ \hline C_2 &&&&&& \times \\ \hline \end{array}$

Also, why do you make the distinction new acquaintance?
. . Did the couples just meet for the first time?
. . (No, $A_1$ already knows the other five people.)

Give us the original wording of the problem . . . please!