Introduction

At the annual meeting of Board of Directors of Acme Inc. If everyone attending shakes hands exactly one time with every other attendee, how many handshakes are there?

Input and Output Format

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2
3
4
5
6
7

# Input:
2
1
2
# Output:
0
1

{: file="Input and Output” }

Process

This is a math challenge. So using the primitive way of counting, I counted the number of handshakes for each number of attendees, I came up with this:

n  = 1 2 3 4 5
HS = 0 1 3 6 10

where HS is the number of handshakes.

So, the interval between each number of handshake is 1, 2, 3, 4, 5. With this, I was able to come up with a simple formula to calculate the number of handshakes with respect to the number of attendees n:

$$
HS_n = \frac{n(n-1)}{2}
$$

Code

This formula could be use as the return value of the function int numberOfHandshakes(int n), shown below.

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2
3

int handshake(int n) {
    return n*(n-1)/2;
}

{: file="Handshake.c” }

Afterthoughts

This is a pretty simple challenge that allows me to practice sequence counting, I was able to apply what I’ve learnt in this challenge.