problem-solving

---

name: problem-solving description: Use this skill when approaching complex or ambiguous problems, breaking down large challenges, applying first principles thinking, or structuring your approach to a new problem. Trigger on keywords: how do I approach, I don't know where to start, complex problem, break this down, first principles, problem decomposition, stuck on, overwhelmed by.

Problem Solving

Core Mindset

Don't solve the problem you think you have. Solve the problem you actually have.

Most wasted effort in software comes from solving the wrong problem confidently. The first step is always to verify the problem definition.

---

The Problem-Solving Framework

1. DEFINE    — What is the actual problem? (not the symptom)
2. CONSTRAIN — What are the boundaries? (must-haves, non-negotiables)
3. DECOMPOSE — Break into smaller sub-problems
4. EXPLORE   — Generate multiple approaches before committing
5. DECIDE    — Choose based on explicit criteria
6. EXECUTE   — Implement the chosen approach
7. REVIEW    — Did it solve the right problem?

---

First Principles Thinking

Instead of reasoning by analogy ("how do others do this?"), break the problem down to fundamental truths:

1. What do we know for certain is true about this problem?
2. What assumptions am I making that might be wrong?
3. If I had to rebuild this from scratch knowing only those truths, 
   what would I build?

Use when: existing solutions feel wrong, you're stuck in conventional thinking, or you need a breakthrough.

---

Decomposition Techniques

Top-Down

Start with the goal, break into sub-goals:

Goal: Build a user auth system
└── Registration flow
    ├── Form validation
    ├── Password hashing
    └── Email verification
└── Login flow
    ├── Credential verification
    ├── Session/token creation
    └── Remember me
└── Security hardening
    ├── Rate limiting
    ├── Brute force protection
    └── Audit logging

MECE (Mutually Exclusive, Collectively Exhaustive)

Ensure sub-problems don't overlap and together cover the whole problem.

---

When You're Stuck

1. Restate the problem in different words
2. Ask "what would need to be true" for each possible solution to work
3. Invert — what would make this definitely fail? Design away from that.
4. Simplify — solve a simpler version first, then generalize
5. Time-box exploration — 30 min max before asking for help

---

Trade-Off Analysis

For every major decision, document:

Option A: [description]
  Pros: [benefits]
  Cons: [costs/risks]
  Best when: [conditions]

Option B: [description]
  Pros: [benefits]
  Cons: [costs/risks]
  Best when: [conditions]

Decision: [chosen option]
Reason: [why this fits the current constraints]
Revisit if: [conditions that would change the decision]