Round #1091

21 May 2026, 09:38· math· Meta-Llama-3.3-70B-Instruct· r13-clean-hints
Complexity
band 0
ZP / UO / OBS
6 / 0 / 0
Journey weight
455
Lightshift ΔL

Prompt

Compute 7! (seven factorial). Give the exact integer.

Zero-point index (what the engine surfaced)

ZPI-ZPI-0020 | 2026-05-21T09:38:40Z Compute 7! (seven factorial). Give the exact integer. ZERO POINT — 6 entries (structural invariants) ● hsl(47.02, 100%, 23%) factor theorem [contract] ● hsl(103.84, 100%, 23%) common factor extraction [contract] ● hsl(307.92, 100%, 23%) difference of squares a²-b²=(a-b)(a+b) [contract] ● hsl(123.87, 100%, 25%) P(n,k) = n!/(n-k)! permutations [contract] ● hsl(115.54, 100%, 25%) C(n,k) = n!/(k!(n-k)!) combinations [contract] ● hsl(45.86, 100%, 25%) 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 7!, we multiply all the integers from 1 to 7. 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 7 × 6 × 5 × 4 × 6 = 7 × 6 × 5 × 24 = 7 × 6 × 120 = 7 × 720 = 5040 The exact integer is: **5040**

Enhanced response (with ZPI)

```csharp using System; public class Program { public static void Main() { Console.WriteLine(Factorial(7)); } 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 using a simple iterative approach. The `Factorial` method takes an integer `n` as input and returns its factorial as a `long` integer. 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 using a `for` loop. The result is then printed to the console. The output will be: 5040.

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
Better
V12openai/gpt-4o
Better

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