How to Write Competitive Math Problems

Writing competitive mathematics problems is a fun challenge, but it’s not everyone’s cup of tea. You’ll need to develop a solid understanding of different math topics, such as algebra, geometry, and number theory—a good problem writer crafts challenging and fair questions, ensuring the experience is equitable for all test-takers.

In writing these problems, creativity is paramount. You must take various mathematical concepts and develop them into engaging questions that capture the reader's attention. It is crucial to word your questions precisely, ensuring that the questions are clear and understandable to test takers while remaining engaging. Seeking feedback from a third party is always great for this.

The key concept involved in writing competitive math questions is to craft problems that test the students’ math skills while simultaneously igniting their love for this wonderfully bizarre subject. This inspires test takers to improve their problem-solving skills, guiding them toward creative solutions.

Problem writers often take inspiration from questions that already exist to help them come up with new competitive math questions. They tend to break down these problems to see what works and what doesn’t, and then combine different ideas to create something unique to them. It can be argued that it's impossible to write original questions since every question relies on the same basic math principles. Although this is not entirely wrong, it does miss the point that there are countless ways to combine those principles creatively. By blending various topics of mathematics, you can devise problems that encourage test-takers to think out of their comfort zone.

It is totally fine to get inspiration from others’ work; in fact, it can even lead you to using those concepts from their work in different ways, resulting in exciting challenges. The core principles are always the same, but implementing a creative approach can result in innovative math problems that truly encourage a good understanding of the subject.

As for me, when I started writing these different math problems, I used to use questions from the American Mathematics Competition (AMC), particularly AMC 12, as a starting point for my problems. I would later tweak the numbers and combine ideas from several different questions to make my questions much more intriguing and challenging. After getting a general idea of the concepts used in these problems, I will write a problem. After creating a problem, I always make sure to double-check the accuracy of the problem I created. To attempt these questions, test takers have to think creatively and understand these concepts at a deeper level. They have to work efficiently in finding the fastest way to answer the question without wasting too much time.

Creating a math question needs careful attention to detail. Each problem should be mathematically accurate and challenging enough for the test-takers. Writers also need to tailor their questions to the overall difficulty of the exam.

While picking up existing problems for a competition, it’s important to cherry-pick in a way that caters to the exam's overall theme, then make small adjustments to keep things fresh. Also, the writer should focus on tailoring questions specifically to the skills that the exam aims to test, ensuring that they truly reflect the participants' capabilities. 

You can think of creating a math problem (or any problem for a different subject, for that matter) as baking a cake. For making a cake, you always begin with a foundation, and then carefully layer on different combinations of ingredients on it to make it look and taste delicious. Every consecutive addition to the cake, from sweet fruits to decadent frosting, is chosen with care to build a delightful experience.

To write a good math problem, a person requires a diverse repertoire of skills. It starts with developing amazing critical thinking skills to analyse the issue, requiring a solid grasp of the different mathematical concepts. To have the ability to categorise questions by their themes is important for boosting a focused approach. A creative mindset enables writers to craft one-of-a-kind questions, while possessing strong writing skills serves as a “cherry on top” and is essential for effective communication. In a nutshell, creating math problems (or any problem on different topics, for that matter) involves a blend of analytical thinking, creativity, and clear communication with readers.

Written by Armaan S

Edited by Alex M, Ayush K, and Anvi R