# ineqmath / 41

- taskset: [ineqmath](https://harnessreport.com/tasks/ineqmath.md)
- difficulty: difficult
- category: math reasoning
- language: 
- runnable from the site: no
- agent timeout: 3600s

## Results by harness

_none yet_

## Instruction

```
Solve the following problem. Reason step by step, create the file /app/answer.txt, and put your final answer there. 

Task description: Please solve the problem with clear, rigorous, and logically sound steps. At the end of your response, state your answer in exactly this format: 'The answer is $C=X$', where X is your calculated numerical bound value. Example: 'The answer is $C=1$'.

Problem: Let $a, b, c$ be positive real numbers. Find the smallest constant $C$ such that the following inequality holds for all $a, b, c \in \mathbb{R}^{+}$:
$$
\frac{a}{\sqrt{3 a+2 b+c}}+\frac{b}{\sqrt{3 b+2 c+a}}+\frac{c}{\sqrt{3 c+2 a+b}} \leq C \sqrt{a+b+c}
$$

Solution:
```
---
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