Problem Solving

When solving a problem (as opposed to merely using a given formula), it is generally good to proceed along the following lines:

  1. First, you have to understand the problem.
  2. After understanding, make a plan.
  3. Carry out the plan.
  4. Look back on your work. How could it be better?

Understanding the Problem

Before you begin calculating, it is a good idea to spend some time trying to understand exactly what it is that is being asked. Here are some questions to ask yourself before you begin:

  • What is being asked?
  • Are there terms or definitions in the problems that I don't understand?
  • What information will I need to solve this problem? Is it all present in the question?
  • Can I restate the problem in my own words?
  • What form will a correct answer take?

Make a Plan

There are often many reasonable approaches to solving a problem, and every student has a different apporach. Make a plan that will help you get to the answer. Some possible apporaches:

  • Draw a picture.
  • Solve an equation.
  • Guess and check.
  • Make a list and look for patterns.
  • Solve a simpler problem and see if it sheds light on this one.
  • Look at individual cases.
  • Work backwards from the answer.
  • Use a formula.

Carry out the Plan

This is usually much easier than understanding the problem or making the plan. Proceed forward with patience and care. If you find that your plan has failed or that you did not fully understand the problem before beginning, now is the time to start over and begin again. Don't be afraid to discard a failed plan; keep trying and you will solve it!

Review your Work

Problem solving is a skill that can only be aquired through extensive practice, and one of the things that ensures you continue to progress is actively paying attention to your own work. Did you make any careless mistakes? Was there anything that would have been easier if you'd understood it better? Review your work to make the next problem easier.

Note: these instructions were inspired by How to Solve It by George Pólya.

Note by Arron Kau
6 years, 10 months ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link]( link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}


Sort by:

Top Newest

Good advice. But you must consider that answering questions in exam is much different from doing it this way because of the shortage of time. So can you provide any strategies for that.

Satvik Choudhary - 6 years, 1 month ago

Log in to reply

Well in the beginning it may be boring and frustrating, but if you practice these steps enough times, you surely can do all of these in a minute or two, while seeing the mathematics with a different angle and every angle, and writing the genuine solution, and having a feeling like you have invented the solution.

Devendra Singh - 6 years ago

Log in to reply


Problem Loading...

Note Loading...

Set Loading...