# Counted the number of handshakes that were exchanged

1. Aug 9, 2004

### 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?

2. Aug 9, 2004

### check

A little ambiguous, but 8 people exchanged handshakes. So either 8 guests, or seven guests and one host, or 6 guests and 2 hostsâ€¦ etc.

Reasoning:

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
3. Aug 23, 2004

### 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.

4. Aug 23, 2004

### check

Hence why I wrote, "A little ambiguous".

5. Aug 23, 2004

### Gokul43201

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

6. Aug 24, 2004

### 4newton

a small number