Lesson How to correctly write a problem

This Lesson (How to correctly write a problem) was created by by richard1234(7193)

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About richard1234: BS in mathematics w/ computer science. Previous tutoring experience, and I have participated in the USAMO.

Writing problems in a way that is easy to understand makes it easier for you, us tutors, and also increases the probability that a tutor will provide you with a solution. Problems that are ambiguous, contain zero grammar, submissions that contain 10 problems, or do not contain enough info will likely not be answered. Some tips on writing problems:

1. Post the *entire* problem. Remember we can only see what you wrote, not your entire textbook. Also, never assume that we have a copy of your textbook.
Good problem: If

, what is the value of

?
Bad problem:

Good problem: Let I, O, H denote the incenter, circumenter, and orthocenter of triangle ABC. Prove that I, O, and H are collinear.
Bad problem: Prove that I, O, and H are collinear.

Good problem: What is the y-intercept of

?
Bad problem:

(a linear equation, but what do we do with it?)

Bad problem: I need help with problem 7 on page 28 of (insert textbook here)
Bad problem: What is f(2) + g(2)?
Good problem: What is f(2) + g(2), where f(x) = x^2 if x > 0, f(x) = -x if x <= 0, and g(x) = f(x) + 4 for all x.
2. Use proper grammar. Typing in all caps is not recommended online, and is usually considered rude (especially in emails or forums).
Good problem: What is 1+1?
Bad problem: WHAT IS 1+1????

3. Make sure your problem is not ambiguous and open to several interpretations. If you are typing formulas, use parentheses or use { { { ... } } } to type them. If you know LaTeX, you can use * [ tex (formula) ] (remove spaces). For example,

is typed * [ tex \large x^2 = 25 ] (without spaces). This works for tutors as well!

Good problem: If +%285x%2B1%29%2F%28x%2B2%29+=+10

, what is the value of x?
Good problem: If

, what is the value of x?
Good problem: If (5x+1)/(x+2) = 10, what is the value of x?
Bad problem: If 5x+1/x+2 = 10, what is the value of x? (ambiguous)

In particular, some useful commands in LaTeX that a lot of students may not know:

: x^2

: x^{10}

: \frac{a}{b}

: \sqrt{x}

: \log_a b

: a \choose b or \binom{a}{b}

: \int_{1}^{\infty} \frac{1}{x} \, \mathrm{d}x

If writing a geometry problem that includes a diagram, make sure you provide a picture of the diagram or describe the diagram in depth so that we can interpret the diagram without any confusion.

Bad problem: ABC is an isosceles triangle with

. Points M and N are in the plane such that

and

. Prove that A is the midpoint of MN.
Good problem: ABC is an isosceles triangle with

. Points M and N are in the plane such that

and

, and A is on segment MN. Prove that A is the midpoint of MN.

The reason why the first problem is a bad problem is that the diagram can be drawn in such a way that A is not on MN.

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