Problema Solution

In 1999 a computer macro based on a popular suite of programs was launched through the Internet. This macro came in the form of an email messages that replicated itself via the first 50 email addresses in a recipient's address list. For example, a person A sends the message to person B, who inadvertently sends a copy of the message to the first 50 people in his email address book. Assume that there are no duplicate recipients. If the first email is called the first generation, how many total emails will have been sent in the first five generations?

Answer provided by our tutors

1st generation: 1 
2nd generation: 50
3rd generation: 50^2 = 2,500
4th generation: 50^3 = 125,000
5th generation: 50^4 = 6,250,000

The total sum is:

6,250,000 + 125,000 + 2,500 + 50 + 1 = 6,377,551

A total of 6,377,551 emails have been sent in the first 5 generations.