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

Annotations already declare readOnly/idempotent/non-destructive/non-open-world, so the safety profile is covered. The description adds genuinely useful context beyond them: determinism via seed, daily puzzles rotating at 00:00 UTC, the 50/day free tier, and Bearer-key auth for higher volume. It does not describe response size or pagination, but for a read-only generator that is minor.

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?

Four sentences, front-loaded with what is returned and the guarantee of a unique solution before moving to use cases and pricing. Dense but every sentence carries information; the type/level enumeration is slightly redundant with the enum descriptions.

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?

No output schema exists, so the description must (and does) enumerate the return payload: rules, puzzle JSON, SVG URL, and optional solution, plus the unique-solution guarantee for cage/pyramid. Coverage of params is adequate given 60% schema coverage; only response shape details (e.g., field names) are left to the caller to discover.

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 60%, and the two most important params (seed, type) are already well documented in the schema. The description restates the puzzle types and difficulty levels and implies include_solution ('optionally, the solution') but adds no format or syntax detail beyond what the schema provides. Baseline 3 fits.

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?

States a concrete verb+resource (returns an original number puzzle) and enumerates the three puzzle types and three difficulty levels. The return payload — rules, puzzle JSON, SVG print URL, optional solution — is spelled out, so an agent knows exactly what comes back without opening a schema.

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?

Gives explicit usage contexts ('math practice, classroom warm-ups, puzzle apps or a daily puzzle') and notes the free-tier vs paid-key split, so the agent knows the intended domain. There are no sibling tools, so no alternative-routing guidance is needed, but it stops short of stating when NOT to use it.

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