Problem Statement

Problem Statement

POW 7 describes a situation involving a girl named Leigh and the new rules regarding phone use her parents had just come up with. Leigh‘s parents were concerned about how much time she was spending on the phone, so they decided to limit her phone time from 8 P.M. to P.M. on school nights. Leigh's friends also had the same phone restrictions. In order to spread news more quickly and efficiently, they decided that all they needed was minutes in which they could dial, make a connection, and finish the call. To start, Leigh would call Mike. Then she would call Diane, and he would call someone else. Therefore, no one would be called twice, and no one would ever get a busy signal. In this POW, we were asked to find out how many of Leighs friends would be called between 8 and P.M.

Process

To begin working toward a solution, I figured that I had to write out at least the beginning of the phone tree. I wrote out who Leigh called, and who would call others after being called. I quickly saw the numbers multiply, and soon a pattern could be recognized, but not immediately. I wrote out a chart of the times, 80 for example, and how many people were called, not including Leigh and other who had already been called.

All I had to do was add up the people afterward. The trick to solving this problem was looking at the numbers and attempting to find a pattern in order to more easily solve the problem using an equation, which appeared to be difficult as the numbers grew. I figured that the only way to keep sense of all these numbers was to put it in order by time and keep it in a loose chart formation. I wrote out Leigh and the other people's names that were told to us. As the list grew, I added my own names. This is how I found out that for every minute call, the overall number of people who have heard the gossip information doubles.