Problem Set #4

This is the second blog that I've done for a problem set question, and I chose question number 20. Here is the question.

20. What is the largest positive integer n that satisfies n^200 < 3^500 ?

      (A) 13   (B) 14   (C) 15   (D) 16   (E) 17

This question looks a lot harder than it is. So the first thing that i did when i saw this question was that i out 3^500 into my calculator. Of course, it didn't work, the number was way to big to fit on the screen. After that, i stared at the question for a while, wondering what to do. Then it hit me, i could take the two zeroes off from both sides. I decided to try it, the equation became n^2 < 3^5. It was a lot simpler after that. 3^5 is 243, so i had to find that highest square that didn't go over that. It was 15x15, which was 225. That made the answer 15, which meant it was C.

I like this question because it looked so hard, but it actually wasn't. When i figured out how to solve it, I felt happy because I figured it out.

I learned from this question that it is important to simplify complicated questions into simpler ones so that it is possible for you to solve them. I can apply this to all the other times that I will be doing math and i know that it will help me a lot.

- casie

Field Trip Assignment

Ten things that i learned about math from this field trip.

1.  There are many ways to solve every problem

2. Don't be afraid to try a hard problem

3. Sometimes you need to read over a question many times to get it

4. Don't give up until you try everything

5. Draw diagrams, they help

6. Write equations, they help too

7. Always know how to prove your answer

8. Show your work, it helps to keep track of what you're doing

9. Only guess as your last resort

10. Be sure to understand the question before you start it

From the talk that we got to hear, i learned that the process of finding the answer in a math question is even more important than the actual answer. If you just have the answer, but you don't even know how you got there, it's useless because the you can't prove that you solved the question by yourself. I also learned that being a mathematician is good because you get to discover things, and if you're the first person to find the answer to something, you would feel really good about yourself.

The workshop will help me in the future because it was good practice. I learned that there are many ways to do math, and that you don't always have to stick to one way of doing things because there are many different types of math questions so you can't always use the same methods.

This field trip helped me to understand more about math and learn more about it.

- casie

Problem Set #3

The question that I have chosen to do this blog on is number 11. Here is the question.

11. Let N = 10^3 + 10^4 + 10^5 +10^6 + 10^7 + 10^8 + 10^9. The sum of the digits of N is
       A. 12    B. 1    C. 6    D. 9    E. 7

At first when i saw this question, i was thinking, oh no, I'm going to have to count so many zeros! i started to find out how many zeros were in each exponent, ( eg. 10^3 = 1000, 10^4 = 10000, etc.) but then i realized that the question wasn't asking me what the answer to the equation was, only for the sum of all the digits. After i realized that, i figured out quite easily that no matter how many zeros there are in the equation, there is only going to be one 1. So the sum of the digits would always be one. So that makes the answer one (:


I liked this question because it made me realize that questions that seem to be hard at first can actually turn out to be really easy. I was so happy when i caught my own mistake and was able to solve the problem easily.


Something that i learned from this question is that i should read the whole question first before i rush into it without really knowing what I'm doing. If i had paid more attention to the question at first, then i could have gotten through this question quickly.


- casie