# Handshake problem

• Feb 16th 2010, 02:38 PM
SoConfused14
Handshake problem
I would appreciate some help with this problem.

This is all the information I have --

10 People in a room. Each person shakes hands with 5 people. How many handshakes take place?

I want to say 50 -- but that would seem too easy.

Thank you in advance for your help.
• Feb 17th 2010, 10:14 AM
Quote:

Originally Posted by SoConfused14
I would appreciate some help with this problem.

This is all the information I have --

10 People in a room. Each person shakes hands with 5 people. How many handshakes take place?

I want to say 50 -- but that would seem too easy.

Thank you in advance for your help.

Round 1

Put 5 people standing in a line
The other 5 people shake hands with them, that's 5 handshakes.

Round 2

Let the 5 people in the line stay where they are and move the other 5 onto the next person, with the original first of them moving around to the end.
That's another 5 handshakes.

Continue to rotate the 2nd group to get 5+5+5 more handshakes.

In this way each person shakes hands with 5 other people.
However, that's not the only way.

In total, there are 5(5)=25 unique handshakes.
However, there are alternative versions of these 25 handshakes.