Counted the number of handshakes that were exchanged

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Discussion Overview

The discussion revolves around the problem of determining the number of guests at a gathering based on the total number of handshakes exchanged, which was stated to be 28. Participants explore different interpretations of the problem and the implications of the given information.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that if 8 people exchanged handshakes, then the equation (x^2 - x) / 2 = 28 can be used to solve for x, leading to a conclusion of 8 guests.
  • Another participant argues that the statement "they were a total of 28" could refer to either handshakes or guests, allowing for various interpretations, including the possibility of 28 guests or any number of guests with different handshake patterns.
  • A later reply reiterates the ambiguity of the original statement and emphasizes that the number of guests could be any integer greater than or equal to one, depending on the context of the handshakes.
  • One participant humorously challenges the practicality of having an extremely large number of guests at a "small get-together," suggesting that such a scenario is implausible.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the number of guests, with multiple competing interpretations of the original statement and the implications of the handshake count remaining unresolved.

Contextual Notes

The discussion highlights the ambiguity in the phrasing of the problem, particularly regarding whether "28" refers to handshakes or guests, and the assumptions that participants make based on this interpretation.

vikasj007
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Recently, I attended a small get-together. I counted the number of handshakes that were exchanged. They were a total of 28.

Can you tell me, how many guests were present?
 
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A little ambiguous, but 8 people exchanged handshakes. So either 8 guests, or seven guests and one host, or 6 guests and 2 hosts… etc.

Reasoning:

x # of people shake x # of people's hands, minus x number of people because they don't shake their own hands, divded by 2 to count the number of handshakes of each pair of shaking hands.

So: (x2 - x) / 2 = 28
Solve for x, you get 8.
 
Last edited:
There were 28 guests there.

You even said, "They were a total of 28."

If you meant "they were" to refer to the number of handshakes, then the number of guests could be any integer 1 or larger. If there were 34,183,398,305,588 guests there, maybe just two of them decided to shake hands 28 times.
 
Hence why I wrote, "A little ambiguous".
 
False Prophet said:
There were 28 guests there.

You even said, "They were a total of 28."

If you meant "they were" to refer to the number of handshakes, then the number of guests could be any integer 1 or larger. If there were 34,183,398,305,588 guests there, maybe just two of them decided to shake hands 28 times.

Hmmm... 34,183,398,305,588 guests in a "small get-together" ? You must be from some other planet !
 
a small number
 

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