# Seven People handshakes-Math riddle

Riddles and puzzles often invite us to explore the hidden patterns and connections in everyday situations. Today, we have a classic problem involving seven people who meet and shake hands. The challenge is to calculate the total number of handshakes that take place. Join us on this journey of mathematical discovery.

If seven people meet each other and each shake hands only once with each of the others,

How many handshakes happened?

**Answer: 21**

**Explanation : **

Certainly, let's provide a mathematical explanation for the number of handshakes:

To calculate the total number of handshakes that occur when seven people shake hands as described in the riddle, we can use a summation.

We start with the first person, who shakes hands with six other people. This can be represented as:

1st person shakes hands with 6 people = 6 handshakes

Then, the second person shakes hands with the remaining six people (excluding the first person), so:

2nd person shakes hands with 5 people = 5 handshakes

The third person shakes hands with 4 people:

3rd person shakes hands with 4 people = 4 handshakes

This pattern continues until the last person, who shakes hands with only one person:

7th person shakes hands with 1 person = 1 handshake

Now, to find the total number of handshakes, we simply sum up these individual handshakes:

Total handshakes = 6 + 5 + 4 + 3 + 2 + 1

Total handshakes = 21

Therefore, there are indeed 21 handshakes in total when the seven people follow the described handshake pattern.

Solving this handshake puzzle demonstrates that even everyday interactions can be a source of mathematical intrigue. It's a reminder that math is not just about numbers; it's a tool that helps us understand the world around us. The next time you attend a gathering, you'll have a fun fact to share about the number of handshakes taking place! Happy puzzling!