Saturday, October 8, 2011

POW 4, A Timely Phone Tree

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POW 4, A Timely Phone Tree

Problem Statement

POW 4 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. Leighs 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.


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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 peoples 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.


My solution to the question of how many people would be able to hear the information in one hour is that 1,048,576 people would find out. Also, each time a call is completed, twice the people as before now know the information. This is because each person calls a new person, so 8 people would call 8 other people, or one each. Therefore, the number would double to 16. Those 16 would then call 16 new people and give them the gossip, and the number would double again. This is how, by nine oclock, over 1,000,000 people could potentially know this information. My rule for this is that it is ( ^ # of calls) divided by two. An example of this is at 80 ^ is 8. 8/=4, and 4 people are informed, besides Leigh.


POW 4, A Timely Phone Tree, was an engaging, and educationally worthwhile POW. Unlike other POWs that often seem to be tedious or overly difficult, POW 4s problem intrigued me and I never seemed unhappy work on it. I thought it was a benefit to have this POW right after the Alice unit because we were familiar with exponential equations and patterns, and because I felt that the POW it was easier to do, I was inclined to putting a greater amount of effort into it. I would give myself a B on this POW because I believe I did fairly well on it, even though I did get some help from other groups on solving my answer.

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