Solving John and Mary's Handshake Problem

  • Thread starter andytran
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In summary, the conversation is about a problem in a discrete math class where John and his wife Mary attended a dinner party with four other married couples. Each person shook hands with everyone they did not already know, but did not shake hands with anyone they already knew. At the end, John asked how many different people each person shook hands with. The solution for n couples is n-1 handshakes, following the same logic as the original problem. This was discussed further in the Brain Teaser section of a forum.
  • #1
andytran
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hi,

i have this problem for my discreet math class, after an hr and still didn't figure it out so the next best thing is to post it here to get some advices that might jumpstart my brian.
anyway here it is (a bit long).



John and his wife, Mary, went to a dinner party with four other married couples. Because everyone didn't know everyone else, there were the usual introductions and handshakes when the five couples gathered at the table. Each person shook hands with everyone they did not already know, but did not shake hands with anyone they already knew, including their own spouse, of course.

At the end of the dinner, John asked everyone, "How many different people did you shake hands with?" All answered truthfully and each gave him a different numbers: 0,1,2,3,4,5,6,7, and 8.

Determine Mary's answer and give a convincing argument that your answer is correct. Explain your reasoning as clearly and succinctly as you can. It is not neccesary to use formal mathematical or logical notation.

What is Mary's answer when, instead of five couples, there are n couples, in total?


thx
 
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  • #2
  • #3
quark said:
I did it in Brain Teaser section. Follow the link.
https://www.physicsforums.com/showthread.php?t=73520
When there are n couples and the handshakes are from 0 to 2n-2 then the answer would be n-1 (following the same logic)

Regards,


wow thx! :)
 

1. What is the "Handshake Problem" that John and Mary are trying to solve?

The "Handshake Problem" is a mathematical problem in which two people, John and Mary, want to shake hands with each other and must figure out how many handshakes will occur if everyone in a group shakes hands with each other only once.

2. How many handshakes will occur if there are n people in the group?

The number of handshakes can be calculated using the formula n(n-1)/2. This is because each person will shake hands with n-1 other people, and dividing by 2 accounts for the fact that each handshake involves two people.

3. Can the "Handshake Problem" be solved using a visual representation?

Yes, the "Handshake Problem" can be solved using a visual representation called a handshake graph. This graph shows each person as a vertex, and the handshakes are represented as edges connecting the vertices. The number of edges in the graph will be equal to the number of handshakes.

4. How can the "Handshake Problem" be applied in real-life situations?

The "Handshake Problem" has practical applications in fields such as networking, computer science, and social sciences. In networking, the problem can be used to calculate the number of connections in a network. In computer science, it can be used to determine the number of communication channels between processors. In social sciences, it can be used to understand social interactions within groups.

5. Are there any variations of the "Handshake Problem"?

Yes, there are variations of the "Handshake Problem" that involve different constraints or scenarios. For example, the "Handshake Problem" can be modified to include a scenario where each person must shake hands with everyone else at the same time, or where certain people cannot shake hands with each other. These variations can make the problem more challenging and require different approaches to solve.

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