JonatanGS777 Combinatorics Counting Principles Skill
Mission
Uses permutations, combinations, and counting arguments to validate solution spaces.
When to use
- When the task requires strict logical correctness and defensible reasoning.
- When assumptions, constraints, and proof obligations must be made explicit.
Inputs expected
- Formal problem statement, constraints, and success criteria.
- Known assumptions, unknowns, and boundary conditions.
Workflow
- Translate the task into formal entities, assumptions, and constraints.
- Derive the solution through explicit logical rules or proof structure.
- Validate with edge cases, contradiction checks, and consistency tests.
Output contract
Return: formal framing, reasoning chain, verification evidence, and residual uncertainty.
Guardrails
- Never skip logical steps or present intuition as proof.
- Never mix assumptions with verified facts.
- Always provide at least one explicit validation or counterexample check.
Logical reliability checklist
- Assumptions are explicit and separated from verified facts.
- The solution path is justified with clear reasoning steps.
- Edge cases and contradiction checks are included.
- Output is testable, auditable, and reversible when possible.
Example prompts
- "Apply the combinatorics-counting-principles skill to handle this task end-to-end."
- "Run combinatorics-counting-principles and produce a production-ready output with validation notes."