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IBM

MCP Math Server

by IBM

kaprekar_constant

Calculate the Kaprekar constant for any number of digits to find the fixed point in Kaprekar's routine, where rearranging digits and subtracting yields the same result.

Instructions

Get the Kaprekar constant for a given number of digits. (Domain: arithmetic, Category: iterative_sequences)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
digitsYes
Behavior1/5

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 only states what the tool does without any information on output format, error handling, computational limits, or side effects. This is inadequate for a tool with no structured behavioral hints.

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 extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted verbiage, and the domain/category note is efficiently appended without redundancy.

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 lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not cover behavioral aspects, parameter details, or output expectations, making it insufficient for effective tool invocation in this context.

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 0% description coverage, and the description does not add any parameter semantics. It mentions 'digits' but does not explain valid ranges (e.g., positive integers, typical limits like 2-4 digits), constraints, or examples. With low schema coverage, the description fails to compensate.

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: 'Get the Kaprekar constant for a given number of digits.' It specifies a verb ('Get') and resource ('Kaprekar constant'), and the domain/category context helps. However, it does not explicitly differentiate from sibling tools like 'kaprekar_numbers' or 'kaprekar_sequence', which is a minor gap.

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 and category but does not specify prerequisites, constraints, or compare it to related tools (e.g., 'kaprekar_numbers' or 'kaprekar_sequence'), leaving the agent without usage direction.

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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