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Counted the number of handshakes that were exchanged

  1. Aug 9, 2004 #1
    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?
  2. jcsd
  3. Aug 9, 2004 #2
    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.


    x # of people shake x # of people's hands, minus x number of people because they dont 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: Aug 9, 2004
  4. Aug 23, 2004 #3
    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.
  5. Aug 23, 2004 #4
    Hence why I wrote, "A little ambiguous".
  6. Aug 23, 2004 #5


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    Hmmm... 34,183,398,305,588 guests in a "small get-together" ? You must be from some other planet !!
  7. Aug 24, 2004 #6
    a small number
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