ScorpTech x402 Tools

Rencontres

rencontres

Read-onlyIdempotent

The rencontres number D(n, k), the permutations of n objects with k fixed points. D(n, k) = C(n, k) * !(n-k). D(5, 0) is 44, and D(5, 2) is 20. n runs from 0 to 100, and k runs from 0 to n. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/rencontres

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "n": "<n>",
      "k": "<k>"
    },
    "name": "rencontres"
  }
}

Input Schema

Name	Required	Description	Default
`k`	Yes
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A3.9/5.0

Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare readOnly, idempotent, and non-destructive behavior, lowering the burden. The description adds important behavioral context: the tool is paid ($0.001 USDC per successful call via x402 on Solana) and available over HTTPS at a specific endpoint. It does not describe error handling or output format, but the payment and access details are substantial.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is front-loaded with the core definition and formula, followed by brief examples, ranges, and payment/endpoint details. Every sentence contributes useful information without waste.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a simple two-parameter math tool with no output schema, the description provides enough context to invoke it correctly: definition, formula, examples, parameter ranges, and payment/access details. It could explicitly state the return type (integer) and mention sibling alternatives, but overall it is nearly complete.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

With 0% schema description coverage, the description must compensate. It does so by defining n as the number of objects (0 to 100) and k as the number of fixed points (0 to n), which is more precise than the schema's maximum of 100 for both. The formula and examples further clarify parameter meaning.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly defines the tool as computing the rencontres number D(n, k), the number of permutations of n objects with k fixed points. It includes the formula and example values, making the resource specific. However, it does not explicitly distinguish this tool from closely related siblings such as subfactorial (which computes D(n, 0)).

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines3/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

Usage is implied through the mathematical definition and examples, but there is no explicit guidance on when to choose this tool over alternatives like subfactorial or binom. The domain ranges for n and k add context, but no exclusions or alternative routing are stated.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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