Journeyman Solution Writer

The 2nd stage of writing a solution : Journeyman

Review the guidelines for an Apprentice.

Congratulations on writing up solutions! This is an achievement to be celebrated, so give yourself a pat on the back. Over time, it will become easier for you to clearly communicate complicated ideas to others. Remember that practice makes perfect, so keep at it!

As you can see from the solutions of others, there are many different ways to write a solution. Some of them are expressed clearly and quickly get voted up to the top. These are good examples for us to learn from. A clearly presented solution is easier to read and understand. Your audience will appreciate your effort, and will be more likely to finish reading the entire solution and comprehend your wonderful ideas.


Here are some guidelines for a Journeyman:

1) Write and explain what you mean.

When having a monologue with oneself, it is very easy to converse back and forth, because you inherently understand what you want to say. When having a conversation with someone else, this becomes more challenging, as you have to ensure that the other person's doubts are clarified. This becomes difficult when all you can do is write several paragraphs for them to read, and do not have the ability to respond to their concerns through edits or comments thereafter. We are not mind readers, and unless you write down exactly what you mean, your thoughts will remain stuck in your head.

If you tell your ideas "I just can’t get you out of my head", Everyone else will be "La la la la la la la".  \boxed{ \begin{array} {l }\mbox{If you tell your ideas "I just can't get you out of my head", } \\ \mbox{Everyone else will be "La la la la la la la". } \end{array} }

2) Connect your arguments.

When we combine various pieces of logic together, we often need to check that they are still valid. If the link between your statements is not strong enough, then your argument is a house of cards. Be aware of the requirements and implications of your arguments.

A common example is that squaring an equation could introduce additional solutions, hence we always have to check them against the initial conditions. Likewise, you should avoid dividing by 0, since that is rumored to cause the universe to implode.

 Then I’ll huff, and I’ll puff, and I’ll blow your house in.Not by the hair of my chinny chin chin! \boxed{ \begin{array} {l l} \text{ Then I'll huff, and I'll puff, and I'll blow your house in.} \\ \text{Not by the hair of my chinny chin chin!} \end{array} }

3) State the techniques that you are using.

You may have great familiarity with various techniques, and think that some statements are immediately obvious if you apply the XYZ principle. Your audience may not have the benefit of such an experience, and you can help them out by quickly illuminating the way.

 “Make a left turn 100 meters ahead.” - Siri \boxed{ \text{ “Make a left turn 100 meters ahead.” - Siri} }

4) Be clear about the given conditions.

Remind the reader about the initial conditions when you are about to use them. This can help reduce confusion, especially if they didn't understand the conditions completely, thereby making it easier for them to piece the solution together. For algebra word problems, you should explain how you arrived at the mathematical statements, especially if you chose to add or multiply various terms.

 "Poof! Magic!" makes your proof go poof. \boxed{ \mbox{ "Poof! Magic!" makes your proof go poof.} }

5) Mark the end of your proof and state the conclusion.

This indicates that you have completely answered the question that was stated, and the solution is finished.

Some members like to place their numerical answer in a box, which can be done using the < \boxed{ Answer } > command in Latex, which yields 123 \boxed{123} . To denote the end of a proof, some people write Q.E.D, which stands for Quod Erat Demonstrandum (Latin for "which was to be shown"). I prefer to use a small square, whose latex code is < _\square >, and which appears as _\square.

 Q.E.D. = Quite Easily Done.  \boxed{ \text{ Q.E.D. = Quite Easily Done. } }

Examples of solutions

Having outlined these guidelines, let's look at a few examples. The following solutions were written up for this question:

Do I look quadratic to you?:
The equation x10=7 | x - 10 | = 7 is equivalent to the equation x2+ax+b=0. x^2 + ax + b = 0. What is the value of a+b a+b ?

Let’s look at the following solution:

Solution 1: We have x10=7x -10= 7 and so x=17 x = 17 .
But then, we could also have x=3 x = 3 .
So 173+51=31 - 17 - 3 + 51 = 31 .

How could the above guidelines help us to improve this?

Guideline 1: The author likely meant that "Since x10=7 |x-10| = 7 , we either have x10=7 x-10 = 7 or x10=7 x - 10 = -7 ". However, the way it is currently written, the second statement seems to appear magically from thin air.

Guideline 2: There is no logic between the first and second statement, which questions the validity of the entire argument. It is not clear why the second statement is true.

Guideline 3: If the author started off by stating the property of absolute values, he might realize that the first line isn’t completely correct.

Guideline 4: If the author reminded himself that the question stated x10=7 | x-10| = 7 , he would realize how to substantiate the first 2 statements.

Guideline 5: While this question may result in a correct answer of 31, it doesn’t explain all of the steps. What are the values of aa and bb? Why did he find the sum of 3 numbers when the question asked for the sum of 2 numbers?

Don’t forget to use the guidelines that you learnt as an Apprentice!

Now, let’s compare it to this solution:

Solution 2: By Daniel G.

Absolute value of (x-10)=7 is also equal to (x-10)^2 = 49. Now the problem can be expanded so x^2-20x+100=49. The equation simplifies to x^2-20x+51.
So your a and b are -20 and 51, which gets you answer of 31.

This solution provides the explanations for each of the steps, stating why the equations are equal to each other, and explaining that he expanded the terms to arrive at the algebraic mess, and then simplified it. Daniel started with a slight restatement of the given condition, and chose to bold the final answer, which can be done by typing 31 {^*}{^*}31{^*}{^*} . The mathematical statements are also easily understood and well explained, even without the use of LaTeX.

You can view this solution (and the problem) by clicking on the hyperlink Solution 2. If you enjoyed this solution, remember to vote it up!

Aspire to be better. Proceed on and be an Adept.

Note by Calvin Lin
7 years, 4 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}


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Top Newest

How to Include pictures in our solutions?

Debmeet Banerjee - 5 years, 8 months ago

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When adding a solution (or a problem), you can "Insert an image" which allows you to display an image

Calvin Lin Staff - 5 years, 8 months ago

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Debmeet Banerjee - 5 years, 8 months ago

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If someone has already posted a question before, one cannot post another solution. We can only reply, if others another's to clarify. But while replying, we cannot include pictures. Is there another way to do it , sir? I do not edit the answers to the questions I have already posted.

Ashish Menon - 5 years, 5 months ago

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@Ashish Menon When replying, you can always include pictures using the markdown syntax of

![](url link)

For example, that is how I displayed the image in my above comment.

Calvin Lin Staff - 5 years, 5 months ago

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@Calvin Lin Can we include videos in our answer. Like "IMO Problems Weekly"

Ashish Menon - 5 years, 5 months ago

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@Ashish Menon You can add the link to the video.

Currently, we do not support video display on the site.

Calvin Lin Staff - 5 years, 5 months ago

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How can we attach a photo of the proof? Or can we?

sriraman iyer - 3 years, 2 months ago

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When writing your solution, there should be a symbol on the top of the text box representing a photo. That will allow you to select an image file and upload it to your solution/problem.

Blan Morrison - 3 years, 2 months ago

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how do i add a wiki page link in a problem?

Shrinidhi H M - 3 years, 8 months ago

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Post your solution, then edit it. There should be an option that says something along the lines of "Start typing to find a relevant wiki."

Blan Morrison - 3 years, 6 months ago

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can we post a solution only if we get the correct answer?

saptarshi sen - 5 years, 6 months ago

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Yes. That is to prevent people who got the problem wrong from posting wrong solutions and confusing others.

If you believe that the answer is incorrect, you can report the problem and explain why. If we update the answer to your value, then you will be able to add a solution afterwards.

Calvin Lin Staff - 5 years, 6 months ago

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How can I post photo?

Chirag Gohil - 5 years, 4 months ago

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When you click the image button in the formatting toolbar, you will be asked to select an image to upload.

Calvin Lin Staff - 5 years, 4 months ago

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How can I write arrays?

Soha Farhin Pine Pine - 4 years, 5 months ago

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(For more details, check out our Formatting guide).

If you do not know Latex, this code:

|| 1 || 2 || 3 ||
|| a || b || c ||

produces this:


If you're familiar with LaTex, this code:

\begin{array} { | l | l | l | }    
\hline 1 & 2 & 3 \\   
\hline a & b & c \\   


123abc \begin{array} { | l | l | l | } \hline 1 & 2 & 3 \\ \hline a & b & c \\ \hline \end{array}

Calvin Lin Staff - 4 years, 5 months ago

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Okay, thanks a bunch! And, btw, how to strike through diagonally to show cancellation?

Soha Farhin Pine Pine - 4 years, 5 months ago

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How to strike through diagonally to show cancellation?

Soha Farhin Pine Pine - 4 years, 5 months ago

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Ashish Menon - 4 years, 5 months ago

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How can i write greater than equal to in the solution using latex???

a>b a > b , ab a \geq b

Arindam Paul - 4 years, 1 month ago

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I've edited your comment to add that in. You can click on "edit" to see the Latex.

In addition, you can select "Toggle Latex" from the menu to see the Latex of equations that others have typed up. This makes it easy to learn from existing equations on the site.

Calvin Lin Staff - 4 years, 1 month ago

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How can you edit other's comment?!

Ong Zi Qian - 3 years, 9 months ago

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@Ong Zi Qian As a staff member, I edit comments when

  1. They ask for Latex help. In this case, I will enter in the correct Latex into their comment, so that they can select "edit comment" (on their own comment) to see the syntax.
  2. Undesirable behavior (Minor ones get edited, major ones get deleted)

In general, I do not edit people comments, unless there is a strong reason to do so.

Calvin Lin Staff - 3 years, 9 months ago

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