Counted the number of handshakes that were exchanged

[vikasj007]

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?

 

[check]

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.

 

[False Prophet]

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.

 

[check]

Hence why I wrote, "A little ambiguous".

 

[Gokul43201]

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 !

 

[4newton]

a small number