invexic's Competition Difficulty Guide

A standardized, detailed difficulty metric for competitive math problems.

Available Resources

AMC 10 Difficulty Scale (0–100)

0–10 Very Easy
Example: AMC 10A 2025 #1 Andy and Betsy both live in Mathville. Andy leaves Mathville on his bicycle at $1:30$, traveling due north at a steady $8$ miles per hour. Betsy leaves on her bicycle from the same point at $2:30$, traveling due east at a steady $12$ miles per hour. At what time will they be exactly the same distance from their common starting point?
Immediate, 1-step, minimal reasoning.
11–20 Easy
Example: AMC 10A 2025 #7 When $x^3+x^2+ax+b$ is divided by $x-1$, remainder is 4. Divided by $x-2$, remainder is 6. What is $b-a$?
Straightforward; early AMC problems. They are often conceptual.
21–35 Easy–Medium
Example: AMC 10A 2025 #4 A team of students is going to compete against a team of teachers in a trivia contest. The total number of students and teachers is $15$. Ash, a cousin of one of the students, wants to join the contest. If Ash plays with the students, the average age on that team will increase from $12$ to $14$. If Ash plays with the teachers, the average age on that team will decrease from $55$ to $52$. How old is Ash?
Some structure required; mild trick or observation required.
36–50 Medium
Example: AMC 10A 2025 #9 Let $f(x) = 100x^3 - 300x^2 + 200x$. For how many real numbers $a$ does the graph of $y = f(x - a)$ pass through the point $(1, 25)$?
Multi-step problem-solving, but still approachable.
51–65 Medium–Hard
Example: AMC 10A 2025 # add in later
Non-standard approaches; more involved. Requires more advanced concepts.
66–80 Hard
Example: AMC 10A 2025 # add in later
Later AMC problems; tricky even for advanced contestants.
81–90 Very Hard
Example: AMC 10A 2025 # add in later
Top-end AMC difficulty; requires ingenuity or multiple observations.
91–100 Extremely Hard
Example: AMC 10A 2025 # add in later
AIME-level problem-solving or difficult bashes.

About this Guide

I've detailed five main points for each problem in this difficulty guide: core ideas, non-obvious transitions, techniques, error-prone steps, and time costs.
So far, I've only added in the 2025 AMC10s, and I hope that I can add more problems in the future. Obviously, difficulty is subjective and feel free to challenge any comments that you feel are incorrect.
I noticed the lack of a standardized difficulty metric for past AMC problems, and I hope I can expand to more problems, especially for more underepresented olympiads like USNCO and USAPhO. Students often rely on subjective comments, making study planning inefficient, and I hope with this website I can help contribute to a solution to this problem.
I've detailed my thought process on why I've picked the difficulty level for every problem, and added tags to each problem so you can find similarly categorized problems.

Notes on Ideal Time

For ideal time categories, we define a beginner as averaging under 90s on AMCs, an intermediate contestant as averaging 90-120 on AMCs, and an experienced contestant as averaging over 120 on AMCs. Additionally, this category should not dictate how fast you solve the problem; rather, it should be a benchmark for how fast you should aim to solve the problem.

Credits

Thank you to Alexander Gao, Arjun Raman, Ekansh Malhotra, along with many other novice problem-solvers from the Indiana area for aiding me in this project by contributing opinions towards difficulties.
Heavily inspired by the USACO Guide.