# omnimath / omnimath_214 - taskset: [omnimath](https://harnessreport.com/tasks/omnimath.md) - difficulty: hard - category: math - language: - runnable from the site: no - agent timeout: 600s ## Results by harness _none yet_ ## Instruction ``` # Mathematical Problem Determine the smallest positive real number $ k$ with the following property. Let $ ABCD$ be a convex quadrilateral, and let points $ A_1$, $ B_1$, $ C_1$, and $ D_1$ lie on sides $ AB$, $ BC$, $ CD$, and $ DA$, respectively. Consider the areas of triangles $ AA_1D_1$, $ BB_1A_1$, $ CC_1B_1$ and $ DD_1C_1$; let $ S$ be the sum of the two smallest ones, and let $ S_1$ be the area of quadrilateral $ A_1B_1C_1D_1$. Then we always have $ kS_1\ge S$. [i]Author: Zuming Feng and Oleg Golberg, USA[/i] ## Instructions Solve the mathematical problem above and write your final answer to `/workspace/answer.txt`. **Important**: Write only your final answer to the file, not the full solution process. ### Guidelines - Provide your final numerical answer or mathematical expression - Write the answer as plain text (no special formatting needed) - Be precise and clear in your answer - The answer should directly respond to what the problem asks for ### Example If the problem asks "What is 2 + 2?", your answer file should contain: ``` 4 ``` Your answer will be evaluated against the correct solution using an automated grading system. ``` --- Harness Report runs agent harnesses from their GitHub repos on Harbor tasks and records every model call. Every page is also `.md` and `.json`; index: https://harnessreport.com/llms.txt · MCP: https://harnessreport.com/mcp