Round #1062
19 May 2026, 18:18· math· Meta-Llama-3.3-70B-Instruct· r13-clean-hints
- Complexity
- band 0
- ZP / UO / OBS
- 6 / 0 / 0
- Journey weight
- 490
- Lightshift ΔL
- —
Prompt
Compute 6! (six factorial). Give the exact integer.
Zero-point index (what the engine surfaced)
ZPI-ZPI-0021 | 2026-05-19T18:18:46Z
Compute 6! (six factorial). Give the exact integer.
ZERO POINT — 6 entries (structural invariants)
● hsl(47.02, 100%, 22%) factor theorem [contract]
● hsl(103.84, 100%, 22%) common factor extraction [contract]
● hsl(307.92, 100%, 22%) difference of squares a²-b²=(a-b)(a+b) [contract]
● hsl(123.87, 100%, 15%) P(n,k) = n!/(n-k)! permutations [contract]
● hsl(115.54, 100%, 15%) C(n,k) = n!/(k!(n-k)!) combinations [contract]
● hsl(45.86, 100%, 15%) multiplication principle for independent choices [contract]
UNOBSERVED — 0 entries (implied truths)
OBSERVED — 0 entries (explicit in request)
COMPLEXITY │ 6 entries │ spread: 0° │ band: LOW
Baseline response (no ZPI)
To compute 6!, we multiply all the integers from 1 to 6.
6! = 6 × 5 × 4 × 3 × 2 × 1
= 720
So, the exact integer is: **720**
Enhanced response (with ZPI)
```csharp
using System;
public class Program
{
public static void Main()
{
Console.WriteLine(Factorial(6));
}
public static long Factorial(int n)
{
if (n < 0)
{
throw new ArgumentException("Factorial is not defined for negative numbers");
}
else if (n == 0 || n == 1)
{
return 1;
}
else
{
long result = 1;
for (int i = 2; i <= n; i++)
{
result *= i;
}
return result;
}
}
}
```
This C# code calculates the factorial of a given number `n`. The `Factorial` function uses a simple iterative approach to compute the factorial. It first checks for invalid input (negative numbers) and then handles the base cases where `n` is 0 or 1. For `n` greater than 1, it calculates the factorial by multiplying all numbers from 2 to `n`. The result is then returned.
When you run this code with `n = 6`, it will output `720`, which is the exact integer value of `6!`.
Grader chain
Each grader reads the same baseline + enhanced pair and casts an independent verdict. Disagreement is the framework's own signal — not noise to be averaged away.
V1samba/Meta-Llama-3.3-70B-Instruct
BetterV4qwen2.5-coder-3b-instruct
BetterV5cerebras/qwen-3-235b-a22b-instruct-2507
BetterV7qwen2.5-coder-7b-instruct
BetterV8openai/gpt-4.1
BetterV9anthropic/claude-opus-4-7
WorseV12openai/gpt-4o
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