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
Better
V4qwen2.5-coder-3b-instruct
Better
V5cerebras/qwen-3-235b-a22b-instruct-2507
Better
V7qwen2.5-coder-7b-instruct
Better
V8openai/gpt-4.1
Better
V9anthropic/claude-opus-4-7
Worse
V12openai/gpt-4o
Better

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