POW #1 A timely phone tree
Jordyn Marez
A Timely Phone Tree
Problem Statement:
Leigh’s parents were worried about how much time she was spending talking on the phone so limited her time from 8:00 to 9:00. Leigh’s friends were given the same rule. Leigh and her friends came up with a good way to spread news. After experimenting, they figured out that 3 minutes was the perfect amount of time to get the news around by 9 o’clock. At 8:00, Leigh would call Mike. Then at 8:03, Leigh would call Diane and Mike would call Ana May. After talking, those four would call someone else and so on until 9:00.
Process:
At first, I tried to do a tree of how many people knew at what time and after I got to about 8:12, I stopped and came up with a new way to solve it. I ended up making an in out table to come up with the answer. The in out table was so much easier and a lot easier to keep track of the answers. To get the correct answer, at 8:03, you start off with two people knowing then times 2 by 2 which gives you 4 then times 4 by 2, then 8 by 2, 16 by 2, and so on. By the end, you should have the answer of 1,048,576 people.
Solution:
8:03 → 2 8:18 → 64 8:33 → 2,048 8:48 → 65,536
8:06 → 4 8:21 → 128 8:36 → 4,096 8:51 → 131,072
8:09 → 8 8:24 → 256 8:39 → 8,192 8:54 → 263,144
8:12 → 16 8:27 → 512 8:42 → 16,384 8:57 → 525,288
8:15 → 32 8:30 → 1,024 8:45 → 32,768 9:00 → 1,048,576
By 9:00, 1,048,576 people will know the news.
Self-Assessment and Reflection: Habits of a Mathematician:
The habit I used was staying organized through solving the problem. I had to make my work organized and neat to be able to keep track of my answers. The first way I tried to solve the problem, I knew that I’d end up getting lost and my work wouldn’t be neat at all so when I did the in out table, it was really easy to keep it neat and organized.
A Timely Phone Tree
Problem Statement:
Leigh’s parents were worried about how much time she was spending talking on the phone so limited her time from 8:00 to 9:00. Leigh’s friends were given the same rule. Leigh and her friends came up with a good way to spread news. After experimenting, they figured out that 3 minutes was the perfect amount of time to get the news around by 9 o’clock. At 8:00, Leigh would call Mike. Then at 8:03, Leigh would call Diane and Mike would call Ana May. After talking, those four would call someone else and so on until 9:00.
Process:
At first, I tried to do a tree of how many people knew at what time and after I got to about 8:12, I stopped and came up with a new way to solve it. I ended up making an in out table to come up with the answer. The in out table was so much easier and a lot easier to keep track of the answers. To get the correct answer, at 8:03, you start off with two people knowing then times 2 by 2 which gives you 4 then times 4 by 2, then 8 by 2, 16 by 2, and so on. By the end, you should have the answer of 1,048,576 people.
Solution:
8:03 → 2 8:18 → 64 8:33 → 2,048 8:48 → 65,536
8:06 → 4 8:21 → 128 8:36 → 4,096 8:51 → 131,072
8:09 → 8 8:24 → 256 8:39 → 8,192 8:54 → 263,144
8:12 → 16 8:27 → 512 8:42 → 16,384 8:57 → 525,288
8:15 → 32 8:30 → 1,024 8:45 → 32,768 9:00 → 1,048,576
By 9:00, 1,048,576 people will know the news.
Self-Assessment and Reflection: Habits of a Mathematician:
The habit I used was staying organized through solving the problem. I had to make my work organized and neat to be able to keep track of my answers. The first way I tried to solve the problem, I knew that I’d end up getting lost and my work wouldn’t be neat at all so when I did the in out table, it was really easy to keep it neat and organized.