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IBM

MCP Math Server

by IBM

armstrong_numbers

Identify Armstrong numbers (narcissistic numbers) up to a specified limit. This tool calculates numbers equal to the sum of their own digits each raised to the power of the number of digits.

Instructions

Find all Armstrong numbers (narcissistic numbers) up to limit. (Domain: arithmetic, Category: special_numbers)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
limitYes
Behavior2/5

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions what the tool does but doesn't describe key behaviors: whether it returns a list or sequence, if there are performance considerations for large limits, or what happens with invalid inputs (e.g., negative limits). The description lacks details on output format, error handling, or computational characteristics.

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

Conciseness4/5

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

The description is concise and front-loaded with the core purpose in the first sentence. The second sentence adds domain/category context efficiently. There's no wasted text, and it's appropriately sized for a simple tool, though it could benefit from more detail given the lack of annotations and schema coverage.

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

Completeness2/5

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

Given the complexity (a computational tool with no annotations, 0% schema coverage, and no output schema), the description is incomplete. It doesn't explain the return value (e.g., list of integers), error conditions, or performance implications. For a tool that generates sequences, more context on output behavior is needed to be fully usable.

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

Parameters2/5

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

The input schema has 1 parameter with 0% description coverage, and the description doesn't add any parameter semantics. It mentions 'limit' but doesn't explain its meaning (e.g., inclusive/exclusive, valid range, units). The description fails to compensate for the low schema coverage, leaving the parameter poorly documented.

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 states the tool's purpose: 'Find all Armstrong numbers (narcissistic numbers) up to limit.' It specifies the verb ('Find'), resource ('Armstrong numbers'), and scope ('up to limit'), and distinguishes it from sibling tools like 'is_narcissistic_number' (which tests individual numbers) and 'narcissistic_numbers' (which might generate them differently). However, it doesn't explicitly differentiate from 'narcissistic_numbers' in the sibling list, which could cause ambiguity.

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?

The description implies usage by stating the domain ('arithmetic') and category ('special_numbers'), which provides some context. However, it doesn't give explicit guidance on when to use this tool versus alternatives like 'is_narcissistic_number' (for testing individual numbers) or 'narcissistic_numbers' (a sibling tool with potentially different behavior). No exclusions or prerequisites are mentioned.

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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