Counted the number of handshakes that were exchanged

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SUMMARY

The discussion centers around calculating the number of guests at a gathering based on the total number of handshakes exchanged, which was 28. The formula used is (x^2 - x) / 2 = 28, leading to the conclusion that there were 8 guests present. The ambiguity arises from the interpretation of "28," which could refer to either handshakes or guests, but the consensus is that there were indeed 28 guests at the event.

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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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