Imagine you are at a party with 10 people (including yourself). During the event, each person shakes hands with every other person exactly once. The question is: How many handshakes occur in total?

Objective:
Determine the total number of handshakes that will take place at the party.

Solution

This puzzle can be solved by understanding that each handshake involves a unique pair of people. The key is to calculate the total number of unique pairs that can be formed from the group.

Step-by-Step Solution for Handshake Puzzle:

Step 1: Understand the Pairing Concept

Each handshake occurs between two people. If there are 10 people at the party, the problem is asking for the number of unique pairs of people that can be formed. This is a classic combinatorial problem.

Step 2: Use the Combination Formula

The number of ways to form pairs from a group of people can be calculated using the combination formula:

• Number of pairs = n(n-1) / 2

Where:

• n is the total number of people.

Step 3: Apply the Formula

In this case, with 10 people:

• Number of handshakes = 10(10-1) / 2 = 10 × 9 / 2 = 45

This means that there will be a total of 45 handshakes at the party.

Step 4: Generalize the Solution

If you want to generalize this for any number of people n:

• The formula n(n-1) / 2 can be used to find the number of handshakes in a group of any size.
• For example, if there were 20 people at the party, the number of handshakes would be 20(20-1) / 2 = 190.

Final Answer

At a party with 10 people, there will be a total of 45 handshakes.