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IBM

MCP Math Server

by IBM

kaprekar_numbers

Calculate all Kaprekar numbers up to a specified limit. This tool identifies special numbers where the square can be split into two parts that sum to the original number, useful for mathematical exploration and number theory applications.

Instructions

Find all Kaprekar 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. It states the tool 'finds' numbers, implying a read-only operation, but does not disclose behavioral traits such as performance characteristics (e.g., computational complexity for large limits), output format (e.g., list of integers), or error handling (e.g., invalid limit values). The description adds minimal context beyond the basic purpose.

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 stated first. The additional domain and category information in parentheses is brief and relevant. There is no wasted verbiage, though it could be more structured with explicit sections for usage or parameters.

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 tool's complexity (finding special numbers up to a limit), lack of annotations, no output schema, and low schema coverage, the description is insufficient. It does not explain the return values (e.g., list format), edge cases, or performance considerations, making it incomplete for effective agent use.

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

Parameters3/5

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

The input schema has one parameter ('limit') with 0% description coverage. The description adds meaning by specifying 'up to limit', clarifying that the tool returns numbers less than or equal to this value. However, it does not detail constraints (e.g., limit must be positive) or examples, leaving gaps in parameter understanding.

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 Kaprekar numbers up to limit.' It specifies the verb ('Find'), resource ('Kaprekar numbers'), and scope ('up to limit'). However, it does not explicitly differentiate from sibling tools like 'is_kaprekar_number' or 'kaprekar_sequence', which might handle individual checks or sequences differently.

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

Usage Guidelines2/5

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

The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('special_numbers'), but offers no explicit instructions on prerequisites, when-not-to-use scenarios, or comparisons to sibling tools like 'is_kaprekar_number' for single-number checks.

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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