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

No annotations are provided, so the description carries the full behavioral burden, and it discloses nothing. It does not say whether the result counts ordered arrangements, whether repetition is allowed, what the return format is, or any limits on input magnitude.

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

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

The description is short but wastes its only sentence repeating the title verbatim. Brevity here reflects under-specification rather than efficient editing, leaving an agent with nothing actionable.

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

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

With no output schema, no annotations, and a two-word description, nothing explains the semantics of the computation, expected input form (n and k are typed as strings), or the shape of the result. For a mathematical tool this is completely inadequate.

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

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

Schema description coverage is nominally 100%, so the baseline is 3 even though the description itself says nothing about parameters. The schema entries ('K to process', 'N to process') are near-useless placeholders, but per the coverage heuristic the baseline applies rather than a penalty.

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

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

The description is a bare restatement of the tool name ('Permutation Count: Permutation Count'), which is the definition of a tautology. The name implies counting permutations, but the description adds no verb, no resource context, and no differentiation from the many sibling combinatorial tools such as x402-permutations, x402-combinations, or x402-partition-number.

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

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

There is no guidance whatsoever about when to use this tool versus alternatives. Siblings like x402-permutations and x402-combination-count cover adjacent ground, and nothing in the description tells an agent which to pick or under what conditions.

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