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 delivers none of it: no statement about valid input range, whether the result is exact or approximated, or what the response looks like. A single-sentence tautology for a computation tool with zero structured behavioral metadata is a serious gap.

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 its brevity is under-specification rather than economy: it repeats the name verbatim and front-loads no useful information. Nothing here earns its place.

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?

For a math tool with no annotations and no output schema, the description must explain the computation, its input domain, and the returned value. It explains none of these, leaving the agent unable to call the tool correctly or interpret its result.

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?

The schema technically covers the single parameter, but its text ("N to process") is vacuous, and it types a numeric input as a string with no format or bounds guidance. The description adds nothing to compensate, so the agent still cannot infer what to pass for n.

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?

"Derangement Count: Derangement Count" is a pure tautology that restates the tool name twice and never says what is being computed. An agent cannot tell from this whether it returns the number of permutations with no fixed points, whether it takes a set or an integer n, or how it differs from siblings like x402-permutation-count 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 when-to-use guidance, no mention of the adjacent combinatorial tools (permutation-count, combination-count, bell-number), and no stated input domain or prerequisites. The description gives the agent nothing to route on.

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