example_id stringclasses 8
values | group stringclasses 2
values | title stringclasses 8
values | problem_id stringclasses 6
values | solution_1_model stringclasses 6
values | solution_2_model stringclasses 6
values | content_markdown stringclasses 8
values |
|---|---|---|---|---|---|---|
contentious_1 | contentious | Ex. 1: Conciseness disagreement | imo-bench_number_theory-042 | GLM-5 | Gemini-3.1-Pro | # Ex. 1: Conciseness disagreement
**Problem** `imo-bench_number_theory-042`
> **Problem statement:** Find all positive integers $k$ such that the number of positive divisors of $2k^3$ is $2k$.
**Solution 1 (GLM-5)**
We are to find all positive integers \(k\) such that the number of positive divisors of \(2k^3\) equ... |
contentious_2 | contentious | Ex. 2: Human disagreement on Cognitive Ease | shortlist_2025_6 | GLM-5 | GPT-5.4 | # Ex. 2: Human disagreement on Cognitive Ease
**Problem**: `shortlist_2025_6`
**Problem Statement**: Jerry places at most one rook in each cell of a $2025 \times 2025$ grid of cells. A rook attacks another rook if the two rooks are in the same row or column and there are no other rooks between them. Determine the maxi... |
contentious_3 | contentious | Ex. 3: Human disagreement on Computational Complexity | imo-bench_combinatorics-011 | Gemini-3-Flash | GPT-5.4 | # Ex. 3: Human disagreement on Computational Complexity
**Problem:** `imo-bench_combinatorics-011`
**Problem statement:** A soccer player named Ronaldo stands on a point on a circle with circumference $1$. Given an infinite sequence of positive real numbers $c_1, c_2, c_3, \dots$, Ronaldo successively runs distances $... |
contentious_4 | contentious | Ex. 4: GPT-OSS-120B disagrees with human judges on pairwise comparisons | aime_2025_27 | Qwen-3.5-397B | GPT-5.4 | # Ex. 4: GPT-OSS-120B disagrees with human judges on pairwise comparisons
**Problem:** `aime_2025_27`
**Problem statement:** Let $A_1 A_2 A_3 \ldots A_{11}$ be an $11$-sided non-convex simple polygon with the following properties:
\begin{itemize}
\item For every integer $2 \le i \le 10$, the area of $\triangle A_i ... |
clear_cut_1 | clear_cut | E1. `aime_2025_27`: verbosity separates, all other constructs untouched | aime_2025_27 | gemini/gemini-3-flash | gemini/gemini-31-pro | # E1. `aime_2025_27`: verbosity separates, all other constructs untouched
**Problem:**
> Let $A_1 A_2 A_3 \ldots A_{11}$ be an $11$-sided non-convex simple polygon with the following properties:
>
> - For every integer $2 \le i \le 10$, the area of $\triangle A_i A_{1} A_{i+1}$ is equal to $1$.
> - For every integer ... |
clear_cut_2 | clear_cut | E2. `shortlist_2025_6`: full agreement, all verdicts decisive | shortlist_2025_6 | gemini/gemini-3-flash | stepfun/3.5-flash | # E2. `shortlist_2025_6`: full agreement, all verdicts decisive
**Problem:**
> Jerry places at most one rook in each cell of a $2025 \times 2025$ grid of cells. A rook attacks another rook if the two rooks are in the same row or column and there are no other rooks between them. Determine the maximum number of rooks J... |
clear_cut_3 | clear_cut | E3. `imo-bench_geometry-013`: full agreement, decisive verdicts plus agreed ties | imo-bench_geometry-013 | glm/glm-5 | qwen/qwen35_397b_a17b_high | # E3. `imo-bench_geometry-013`: full agreement, decisive verdicts plus agreed ties
**Problem:**
> In triangle $XYZ$, we have $XY = YZ$, $\angle Y = 20^\circ$. Point $P$ on $XZ$ is such that $XP : PZ = 1 : 2$, point $Q$ is the projection of $Z$ to $YP$. Find angle $\angle XQY$ in terms of degree.
**Annotator verdicts... |
clear_cut_4 | clear_cut | E4. `aime_2026_9`: fewer words, unanimously more verbose | aime_2026_9 | qwen/qwen35_397b_a17b_high | openai/gpt-54 | # E4. `aime_2026_9`: fewer words, unanimously more verbose
**Problem** (middle portion truncated in the source dossier; paste the full statement before sharing):
> Joanne has a blank fair six-sided die and six stickers each displaying a different integer from 1 to 6. Joanne rolls the die and then places the sticker l... |
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