# ineqmath / 81

- 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 (Letter) Symbol', where Letter is one of the given options. Example: 'The answer is (A) $\leq$'.

Problem: Let $a_1, a_2, \ldots, a_n$ be real numbers such that $a_1 + a_2 + \ldots + a_n = 0$ and $\max \{|a_i - a_j| \mid 1 \leq i, j \leq n\} \leq 1$. Consider the following expression:
$$
a_1^2 + a_2^2 + \ldots + a_n^2 \quad () \quad \frac{1}{n}\left[\frac{n}{2}\right]\left[\frac{n+1}{2}\right] 
$$

Determine the correct inequality relation to fill in the blank.

Options:

(A) $\leq$ 

(B) $\geq$

(C) $=$ 

(D) $<$

(E) $>$

(F) None of the above

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