# Solving Maths Problems: Numbers, Symmetries & Groups

• Firepanda
In summary: Anyway, sounds like you're doing well!In summary, the conversation is about two math problems, 1.c) and 1.d), from the Numbers, Symmetries and Groups module in a first year university math class. The individuals involved discuss possible methods for solving the problems, including using a calculator and recognizing repeating patterns. It is mentioned that these problems may be considered basic for a university level course.
Firepanda
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Is 1. c) as simple as i think it is?

I have gone through my notes and can't find anything to do with it, the module for it is Numbers, symmetries and groups, any ideas or do i simple just wack in 13/7 on my calculator and write down the answer?

Also, 1. d) I don't have a method of working that out.

I tried this though:

24/10 + (1)SIGMA(n) 39/(10^2n+1) = 2.43939393939...

But I don't know how to get this into a fraction from here.

Last edited by a moderator:
For (d) the trick is to use the fact that 393939... repeats itself. Let $a=2.4\overline{39}$ and compute $10a,\,1000a$ and subtract them.

a = 161/66 ;) thanks!

So i just assume 1.c) is a question made for a 10 year old?

Or for a nine and a half!

Actually, Firepanda, I think I could have solved all of these problems when I was ten ... or maybe a year or two later, I don't recall exactly. In what class did you run into these? I hope it wasn't "Calculus and Beyond"!

Well I'm 3 weeks into my Numbers, Symmetries and Groups module for 1st year university maths :P These are also assesed questions, so I can't complain :)

Ah ... so maybe they're just making sure that you've got your basics tucked under your belt?

## 1. What are some common strategies for solving math problems involving numbers, symmetries, and groups?

Some common strategies for solving these types of math problems include breaking the problem down into smaller, more manageable parts, using visual aids such as diagrams or graphs, and applying known mathematical principles and formulas.

## 2. Can you provide an example of a math problem that involves numbers, symmetries, and groups?

One example is determining the number of ways to arrange 6 different colored tiles in a row, with the restriction that the colors must alternate and no two adjacent tiles can be the same color. This problem involves numbers (6 tiles), symmetries (alternating colors), and groups (arrangements).

## 3. How can understanding symmetries and groups help in solving math problems?

Understanding symmetries and groups can help in solving math problems by providing a systematic approach to analyzing the problem and identifying patterns. It can also lead to more efficient problem-solving strategies and help in making connections between different mathematical concepts.

## 4. Are there any real-life applications of using numbers, symmetries, and groups in problem-solving?

Yes, there are many real-life applications of using numbers, symmetries, and groups in problem-solving. For example, these concepts are used in cryptography to encode and decode information, in computer graphics to create symmetrical and geometrically pleasing designs, and in physics to describe the symmetries and patterns observed in nature.

## 5. How can I improve my problem-solving skills when it comes to numbers, symmetries, and groups?

One way to improve problem-solving skills in this area is to practice regularly and challenge yourself with a variety of problems. It can also be helpful to seek out resources such as textbooks or online tutorials that provide explanations and examples of different problem-solving strategies. Additionally, collaborating with others and discussing different approaches to solving problems can also improve problem-solving skills.

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