Benchmark AI / Public workspace
OlympiadBench
Mathematics / Science / Multimodal
OlympiadBench evaluates scientific reasoning on Olympiad-level mathematics and physics problems. Its official description lists 8,476 English and Chinese problems with separate text-only and multimodal settings.
Japanese introduction
数学と物理のオリンピック水準の問題で、科学的推論を評価するベンチマークです。公式紹介では英語・中国語の8,476問を収録し、テキストのみと画像付きの設定を区別します。
olympiadbench
Full text: eligible public problems include text, images and discussion.
Tasks
Whole public benchmark.
- Public problems
- 200
- Formats
- text (200)
- Problems with images
- 0
- Answer availability
- Answer published by the source (200)
- Configs
- OE_TO_maths_en_COMP (200)
- Splits
- train (200)
- Awaiting a first discussion
- 200
- Given a positive integer n, determine the largest real number μ satisfying…
Answer published by the source
- For a positive integer a, define a sequence of integers x₁,x₂,……
Answer published by the source
- Find all positive integers n, for which the numbers in the set …
Answer published by the source
- Determine all pairs (f,g) of functions from the set of positive integers to…
Answer published by the source
- Determine the greatest positive integer k that satisfies the following…
Answer published by the source
- On a square table of 2011 by 2011 cells we place a finite number of napkins that…
Answer published by the source
- On some planet, there are 2^(N) countries (N≥4). Each country has a…
Answer published by the source
- Find all pairs (m,n) of nonnegative integers for which
Answer published by the source
- Determine the largest N for which there exists a table T of integers with…
Answer published by the source
- Let n be a positive integer. Determine the smallest positive integer k with…
Answer published by the source
- Define P(n)=n²+n+1. For any positive integers a and b, the set
Answer published by the source
- Denote by N the set of all positive integers. Find all functions …
Answer published by the source
- Players A and B play a game on a blackboard that initially contains 2020…
Answer published by the source
- There are 60 empty boxes B₁,…,B₆₀ in a row on a table and an…
Answer published by the source
- For any two different real numbers x and y, we define D(x,y) to be the…
Answer published by the source
- For a finite set A of positive integers, we call a partition of A into two…
Answer published by the source
- Determine all triples (a,b,c) of positive integers for which ab−c,bc−a,…
Answer published by the source
- Determine all functions f:Z→Z satisfying
Answer published by the source
- Consider all polynomials P(x) with real coefficients that have the following…
Answer published by the source
- A number is called Norwegian if it has three distinct positive divisors whose…
Answer published by the source
- Find all positive integers n>2 such that
Answer published by the source
- Let k be a positive integer. The organising committee of a tennis tournament…
Answer published by the source
- Let Z_(>0) be the set of positive integers. Find all functions …
Answer published by the source
- Let ABC be a triangle with AB=AC. The angle bisectors of A and B…
Answer published by the source
- In the plane we consider rectangles whose sides are parallel to the coordinate…
Answer published by the source
- Let n≥1 be an integer. What is the maximum number of disjoint pairs of…
Answer published by the source
- In a 999×999 square table some cells are white and the remaining ones…
Answer published by the source
- Players A and B play a game with N≥2012 coins and 2012 boxes arranged…
Answer published by the source
- Let m be a positive integer. Consider a 4m×4m array of square unit…
Answer published by the source
- Find all triples (a,b,c) of real numbers such that ab+bc+ ca=1 and
Answer published by the source
- Determine all integer values of x such that…
Answer published by the source
- What is the value of x such that log₂(log₂(2x−2))=2 ?
Answer published by the source
- Let f(x)=2^(kx)+9, where k is a real number. If f(3):f(6)=1:3,…
Answer published by the source
- Determine, with justification, all values of k for which y=x²−4 and…
Answer published by the source
- Determine all values of x for which …
Answer published by the source
- Let ⌊x⌋ denote the greatest integer less than or equal to x.…
Answer published by the source
- A goat starts at the origin (0,0) and then makes several moves. On move 1 , it…
Answer published by the source
- If f(x)=sin²x−2sinx+2, what are the minimum and maximum values of…
Answer published by the source
- Qing is twice as old as Rayna. Qing is 4 years younger than Paolo. The average…
Answer published by the source
- For some real numbers m and n, the list 3n²,m²,2(n+1)²…
Answer published by the source
- Chinara starts with the point (3,5), and applies the following three-step…
Answer published by the source
- Suppose that n>5 and that the numbers …
Answer published by the source
- Suppose that a=5 and b=4. Determine all pairs of integers (K,L) for which…
Answer published by the source
- Consider the following system of equations in which all logarithms have base 10:
Answer published by the source
- A Skolem sequence of order n is a sequence …
Answer published by the source
- Determine all integers k, with k≠0, for which the parabola with…
Answer published by the source
- A geometric sequence has first term 10 and common ratio (1)/(2).
Answer published by the source
- Four tennis players Alain, Bianca, Chen, and Dave take part in a tournament in…
Answer published by the source
- A bag contains 40 balls, each of which is black or gold. Feridun reaches into…
Answer published by the source
- If log₁₀x=3+log₁₀y, what is the value of (x)/(y) ?
Answer published by the source