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AMC (AIMO validation set)
Mathematics
83 AMC 12 problems assembled by Project Numina as a validation set for the AIMO competition. They sit a step below AIME in difficulty, which makes them a useful lower rung on the same scale.
amc
Full text: eligible public problems include text, images and discussion.
History
Project Numina assembled this AMC validation set for the AIMO competition, publishing it under AI-MO on Hugging Face in July 2024. It uses AMC 12 competition problems to assess mathematical problem solving at a level below AIME, providing a less demanding complement to harder competition evaluations.
How it was built
The set contains 83 existing AMC 12 problems, rather than questions newly written for evaluating language models. Each record pairs a problem statement with a numeric answer and identifies an upstream Art of Problem Solving page. The catalogue includes all 83 problems, while excluding answers and solution-bearing upstream pages from the prompt.
At a glance
What a problem looks like
One competition problem statement. The numeric answer is not part of the prompt, and neither is the Art of Problem Solving page, which is recorded as the problem’s upstream identifier because that page also carries a solution.
How it is scored
The source ships the numeric answer with every problem; this catalogue keeps it in restricted storage and never renders it.
Why it is hard
AMC problems reward a single clean idea rather than a long construction, so failures here point at missing technique rather than at lost arithmetic.
Limitations and criticism
This is a small selection of competition mathematics, so a handful of outcomes can substantially change an aggregate score. Its existing problems and publicly available solution pages create a potential route for training-data contamination, although their availability alone does not establish exposure by any particular model. Numeric-answer evaluation also leaves the validity of the intermediate reasoning unmeasured.
Reference links
Discussion
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Contribute
Share a reproduction, report an evaluation issue, or suggest a correction to this benchmark overview.
Tasks
Whole public benchmark.
- Public problems
- 83
- Formats
- math (83)
- Problems with images
- 0
- Answer availability
- Answer published by the source (83)
- Configs
- default (83)
- Splits
- train (83)
- Awaiting a first discussion
- 83
- Problems with a discussion
- 0
- Public contributions
- 0
Provenance and terms
Pinned source revisions, newest first:
69d78a4a2c840e82d69af6bc742bda09005f6316· acquired 2026-09-12 · releasef88229dded3569d78a4a2c840e82d69af6bc742bda09005f6316· acquired 2026-09-12 · release4078a47d8a6269d78a4a2c840e82d69af6bc742bda09005f6316· acquired 2026-09-12 · release920cd2975153
- (m)/(n) is the Irreducible fraction value of 3+(1)/(3+(1)/(3+(1)/(3))), what is the value of m+n?
Answer published by the source
- What is the value of (log5)³+(log20)³+(log8)(log0.25) where log denotes the base-ten logarithm?
Answer published by the source
- The roots of the polynomial 10x³−39x²+29x−6 are the height, length, and width of a rectangular box (right rectangular prism). A new rectangular box is formed by lengthening each ed…
Answer published by the source
- Suppose a is a real number such that the equation a⋅(sinx+sin(2x))=sin(3x) has more than one solution in the interval (0,π). The set of all such a that can be written in the form …
Answer published by the source
- Let T_(k) be the transformation of the coordinate plane that first rotates the plane k degrees counterclockwise around the origin and then reflects the plane across the y-axis. Wha…
Answer published by the source
- The sum of three numbers is 96. The first number is 6 times the third number, and the third number is 40 less than the second number. What is the absolute value of the difference b…
Answer published by the source
- Let h_(n) and k_(n) be the unique relatively prime positive integers such that (1)/(1)+(1)/(2)+(1)/(3)+⋯+(1)/(n)=(h_(n))/(k_(n)). Let L_(n) denote the least common multiple of the …
Answer published by the source
- How many strings of length 5 formed from the digits 0, 1, 2, 3, 4 are there such that for each j∈{1,2,3,4}, at least j of the digits are less than j? (For example, 02214 satisfies …
Answer published by the source
- A circle with integer radius r is centered at (r,r). Distinct line segments of length c_(i) connect points (0,a_(i)) to (b_(i),0) for 1≤i≤14 and are tangent to the circle, where …
Answer published by the source
- The textit{taxicab distance} between points (x₁,y₁) and (x₂,y₂) in the coordinate plane is given by |x₁−x₂|+|y₁−y₂|. For how many points P with integer coordinates is the taxicab d…
Answer published by the source
- The infinite product
Answer published by the source
- On Halloween 31 children walked into the principal's office asking for candy. They can be classified into three types: Some always lie; some always tell the truth; and some alterna…
Answer published by the source
- Define xdiamond y to be |x−y| for all real numbers x and y. What is the value of ((1diamond2)diamond3)-(1diamond(2diamond3))?
Answer published by the source
- Let f(n)=((−1+i√(3))/(2))^(n)+((−1−i√(3))/(2))^(n), where i=√(−1). What is f(2022)?
Answer published by the source
- The diagram below shows a rectangle with side lengths 4 and 8 and a square with side length 5. Three vertices of the square lie on three different sides of the rectangle, as shown.…
Answer published by the source
- The graph of y=x²+2x−15 intersects the x-axis at points A and C and the y-axis at point B. What is the numerator of the simplest fraction that represents tan(∠ABC)?
Answer published by the source
- In △ABC medians (AD)¯ and (BE)¯ intersect at G and △AGE is equilateral. Then cos(C) can be written as (m√(p))/(n), where m and n are relatively prime positive integers and p is a p…
Answer published by the source
- In rhombus ABCD, point P lies on segment (AD)¯ so that (BP)¯ ⊥ (AD)¯, AP=3, and PD=2. What is the area of ABCD? (Note: The figure is not drawn to scale.)
Answer published by the source
- Let S be the set of circles in the coordinate plane that are tangent to each of the three circles with equations x²+y²=4, x²+y²=64, and (x−5)²+y²=3. What is the sum of the areas of…
Answer published by the source
- Ant Amelia starts on the number line at 0 and crawls in the following manner. For n=1,2,3, Amelia chooses a time duration t_(n) and an increment x_(n) independently and uniformly a…
Answer published by the source
- Four regular hexagons surround a square with side length 1, each one sharing an…
Answer published by the source
- How many of the first ten numbers of the sequence 121,11211,1112111,… are prime numbers?
Answer published by the source
- For how many values of the constant k will the polynomial x²+kx+36 have two distinct integer roots?
Answer published by the source
- What is the sum of the x and y coordinates of the new position of the point…
Answer published by the source
- Camila writes down five positive integers. The unique mode of these integers is…
Answer published by the source
- Cities A and B are 45 miles apart. Alicia lives in A and Beth lives in B. Alicia bikes towards B at 18 miles per hour. Leaving at the same time, Beth bikes toward A at 12 miles per…
Answer published by the source
- Positive real numbers x and y satisfy y³=x² and (y−x)²=4y². What is x+y?
Answer published by the source
- What is the degree measure of the acute angle formed by lines with slopes 2 and (1)/(3)?
Answer published by the source
- In a table tennis tournament every participant played every other participant…
Answer published by the source
- Flora the frog starts at 0 on the number line and makes a sequence of jumps to…
Answer published by the source
- What is the product of all solutions to the equation
Answer published by the source
- The weight of (1)/(3) of a large pizza together with 3(1)/(2) cups of orange slices is the same as the weight of (3)/(4) of a large pizza together with (1)/(2) cup of orange slices…
Answer published by the source
- Rows 1, 2, 3, 4, and 5 of a triangular array of integers are shown below.
Answer published by the source
- If A and B are vertices of a polyhedron, define the distance d(A,B) to be the minimum number of edges of the polyhedron one must traverse in order to connect A and B. For example, …
Answer published by the source
- How many ordered pairs of positive real numbers (a,b) satisfy the equation
Answer published by the source
- Let K be the number of sequences A₁, A₂, …, A_(n) such that n is a positive integer less than or equal to 10, each A_(i) is a subset of {1,2,3,…,10}, and A_(i−1) is a subset of …
Answer published by the source
- There is a unique sequence of integers a₁,a₂,⋯a₂₀₂₃ such that
Answer published by the source
- How many positive perfect squares less than 2023 are divisible by 5?
Answer published by the source
- Points A and B lie on the graph of y=log₂x. The midpoint of (AB)¯ is (6,2). What is the positive difference between the x-coordinates of A and B? The final answer can be written in…
Answer published by the source
- In the xy-plane, a circle of radius 4 with center on the positive x-axis is tangent to the y-axis at the origin, and a circle with radius 10 with center on the positive y-axis is t…
Answer published by the source
- Calculate the maximum area of an isosceles trapezoid that has legs of length 1 and one base twice as long as the other. The final answer can be written in the form (m)/(n), where m…
Answer published by the source
- For how many ordered pairs (a,b) of integers does the polynomial x³+ax²+bx+6 have 3 distinct integer roots?
Answer published by the source
- Triangle ABC has side lengths in arithmetic progression, and the smallest side has length 6. If the triangle has an angle of 120^(∘), Find the area of ABC. The final answer can be …
Answer published by the source
- Carlos went to a sports store to buy running shoes. Running shoes were on sale,…
Answer published by the source
- When n standard six-sided dice are rolled, the product of the numbers rolled can be any of 936 possible values. What is n?
Answer published by the source
- Suppose that a, b, c and d are positive integers satisfying all of the following relations. abcd=2⁶⋅3⁹⋅5⁷ lcm(a,b)=2³⋅3²⋅5³ lcm(a,c)=2³⋅3³⋅5³ lcm(a,d)=2³⋅3³⋅5³ lcm(b,c)=2¹⋅3³⋅5² …
Answer published by the source
- You are playing a game. A 2×1 rectangle covers two adjacent squares (oriented either horizontally or vertically) of a 3×3 grid of squares, but you are not told which two squares ar…
Answer published by the source
- For how many integers n does the expression√((log(n²)−(logn)²)/(logn−3))represent a real number, where log denotes the base 10 logarithm?
Answer published by the source
- How many nonempty subsets B of 0,1,2,3,⋯,12 have the property that the number of elements in B is equal to the least element of B? For example, B=4,6,8,11 satisfies the condition.
Answer published by the source
- What is the area of the region in the coordinate plane defined by
Answer published by the source