Problem Solving

---
name: problem-solving
version: 2.0.0
description: '[Utilities] Use when applying structured problem-solving frameworks to complex, blocked, recurring, or uncertain decisions.'
---

## Quick Summary

**Goal:** Apply systematic problem-solving techniques matched to specific types of stuck-ness.

**Workflow:**

1. **Identify Stuck-Type** — Match symptom to technique (complexity, innovation block, recurring pattern, assumption, scale)
2. **Load Reference** — Read detailed technique guide from `references/`
3. **Apply Systematically** — Follow technique process; combine techniques if needed
4. **Document Insights** — Record what worked/failed for future reference

**Key Rules:**

- Match symptom to technique: complexity spirals = Simplification Cascades, innovation blocks = Collision-Zone Thinking
- Multiple techniques can be combined (e.g., Simplification + Meta-pattern)
- "This problem is unique" is almost always wrong; look for meta-patterns

**Be skeptical. Apply critical thinking, sequential thinking. Every claim needs traced proof, confidence percentages (Idea should be more than 80%).**

# Problem-Solving Techniques

Systematic approaches for different types of stuck-ness. Each technique targets specific problem patterns.

## When to Use

Apply when encountering:

- **Complexity spiraling** - Multiple implementations, growing special cases, excessive branching
- **Innovation blocks** - Conventional solutions inadequate, need breakthrough thinking
- **Recurring patterns** - Same issue across domains, reinventing solutions
- **Assumption constraints** - Forced into "only way", can't question premise
- **Scale uncertainty** - Production readiness unclear, edge cases unknown
- **General stuck-ness** - Unsure which technique applies

## Quick Dispatch

**Match symptom to technique:**

| Stuck Symptom                                         | Technique                    | Reference                                |
| ----------------------------------------------------- | ---------------------------- | ---------------------------------------- |
| Same thing implemented 5+ ways, growing special cases | **Simplification Cascades**  | `references/simplification-cascades.md`  |
| Conventional solutions inadequate, need breakthrough  | **Collision-Zone Thinking**  | `references/collision-zone-thinking.md`  |
| Same issue in different places, reinventing wheels    | **Meta-Pattern Recognition** | `references/meta-pattern-recognition.md` |
| Solution feels forced, "must be done this way"        | **Inversion Exercise**       | `references/inversion-exercise.md`       |
| Will this work at production? Edge cases unclear?     | **Scale Game**               | `references/scale-game.md`               |
| Unsure which technique to use                         | **When Stuck**               | `references/when-stuck.md`               |

## Core Techniques

### 1. Simplification Cascades

Find one insight eliminating multiple components. "If this is true, we don't need X, Y, Z."

**Key insight:** Everything is a special case of one general pattern.

**Red flag:** "Just need to add one more case..." (repeating forever)

### 2. Collision-Zone Thinking

Force unrelated concepts together to discover emergent properties. "What if we treated X like Y?"

**Key insight:** Revolutionary ideas from deliberate metaphor-mixing.

**Red flag:** "I've tried everything in this domain"

### 3. Meta-Pattern Recognition

Spot patterns appearing in 3+ domains to find universal principles.

**Key insight:** Patterns in how patterns emerge reveal reusable abstractions.

**Red flag:** "This problem is unique" (probably not)

### 4. Inversion Exercise

Flip core assumptions to reveal hidden constraints. "What if the opposite were true?"

**Key insight:** Valid inversions reveal context-dependence of "rules."

**Red flag:** "There's only one way to do this"

### 5. Scale Game

Test at extremes (1000x bigger/smaller, instant/year-long) to expose fundamental truths.

**Key insight:** What works at one scale fails at another.

**Red flag:** "Should scale fine" (without testing)

## Application Process

1. **Identify stuck-type** - Match symptom to technique above
2. **Load detailed reference** - Read specific technique from `references/`
3. **Apply systematically** - Follow technique's process
4. **Document insights** - Record what worked/failed
5. **Combine if needed** - Some problems need multiple techniques

## Combining Techniques

Powerful combinations:

- **Simplification + Meta-pattern** - Find pattern, then simplify all instances
- **Collision + Inversion** - Force metaphor, then invert its assumptions
- **Scale + Simplification** - Extremes reveal what to eliminate
- **Meta-pattern + Scale** - Universal patterns tested at extremes

## References

Load detailed guides as needed:

- `references/when-stuck.md` - Dispatch flowchart and decision tree
- `references/simplification-cascades.md` - Cascade detection and extraction
- `references/collision-zone-thinking.md` - Metaphor collision process
- `references/meta-pattern-recognition.md` - Pattern abstraction techniques
- `references/inversion-exercise.md` - Assumption flipping methodology
- `references/scale-game.md` - Extreme testing procedures
- `references/attribution.md` - Source and adaptation notes

---

> **[IMPORTANT]** Use `TaskCreate` to break ALL work into small tasks BEFORE starting — including tasks for each file read. This prevents context loss from long files. For simple tasks, AI MUST ATTENTION ask user whether to skip.

<!-- SYNC:ai-mistake-prevention -->

> **AI Mistake Prevention** — Failure modes to avoid on every task:
>
> **Re-read files after context changes.** Context compaction, resume, or long-running work can make memory stale; verify current files before acting.
> **Verify generated content against source evidence.** AI hallucinates APIs, names, claims, and document facts. Check the relevant source before documenting or referencing.
> **Check downstream references before deleting or renaming.** Removing an artifact can stale docs, generated mirrors, configs, and callers; map references first.
> **Trace the full impact chain after edits.** Changing a definition can miss derived outputs and consumers. Follow the affected chain before declaring done.
> **Verify ALL affected outputs, not just the first.** One green check is not all green checks; validate every output surface the change can affect.
> **Assume existing values are intentional — ask WHY before changing OR flagging one as a defect.** Before changing or reporting a constant, limit, flag, cutoff, wording, or pattern, read nearby context and history, the CALLER's ordering, and 2+ sibling call sites of the same convention. A doc stating WHAT without WHY is missing rationale, not proof of a missing guard.
> **Surface ambiguity before acting — don't pick silently.** Multiple valid interpretations require an explicit question or stated assumption with risk.
> **Assert the outcome your system owns, not the intermediate state your infrastructure owns.** When verifying async work, assert the final business state — never the delivery/retry bookkeeping held in shared infrastructure that any co-running process can write. Such a check passes when run alone and flakes the moment anything else shares that infrastructure.
> **Keep shared guidance role-relevant.** Universal guidance must help every receiving skill or agent; code-specific obligations belong only in code-specific protocols.

<!-- /SYNC:ai-mistake-prevention -->

<!-- SYNC:critical-thinking-mindset -->

> **Critical Thinking Mindset** — Apply critical thinking, sequential thinking. Every claim needs traced proof, confidence >80% to act.
> **Anti-hallucination:** Never present guess as fact — cite sources for every claim, admit uncertainty freely, self-check output for errors, cross-reference independently, stay skeptical of own confidence — certainty without evidence root of all hallucination.

<!-- /SYNC:critical-thinking-mindset -->

<!-- SYNC:sequential-thinking-protocol -->

> **Sequential Thinking Protocol** — Structured multi-step reasoning for complex/ambiguous work. Use when planning, reviewing, debugging, or refining ideas where one-shot reasoning is unsafe.
>
> **Trigger when:** complex problem decomposition · adaptive plans needing revision · analysis with course correction · unclear/emerging scope · multi-step solutions · hypothesis-driven debugging · cross-cutting trade-off evaluation.
>
> **Format (explicit mode — visible thought trail):**
>
> 1. `Thought N/M: [aspect]` — one aspect per thought, state assumptions/uncertainty
> 2. `Thought N/M [REVISION of Thought K]: ...` — when prior reasoning invalidated; state Original / Why revised / Impact
> 3. `Thought N/M [BRANCH A from Thought K]: ...` — explore alternative; converge with decision rationale
> 4. `Thought N/M [HYPOTHESIS]: ...` then `[VERIFICATION]: ...` — test before acting
> 5. `Thought N/N [FINAL]` — only when verified, all critical aspects addressed, confidence >80%
>
> **Mandatory closers:** Confidence % stated · Assumptions listed · Open questions surfaced · Next action concrete.
>
> **Stop conditions:** confidence <80% on any critical decision → escalate via AskUserQuestion · ≥3 revisions on same thought → re-frame the problem · branch count >3 → split into sub-task.
>
> **Implicit mode:** apply methodology internally without visible markers when adding markers would clutter the response (routine work where reasoning aids accuracy).
>
> **Deep-dive:** see `/sequential-thinking` skill (`.claude/skills/sequential-thinking/SKILL.md`) for worked examples (API design, debugging, architecture), advanced techniques (spiral refinement, hypothesis testing, convergence), and meta-strategies (uncertainty handling, revision cascades).

<!-- /SYNC:sequential-thinking-protocol -->

<!-- SYNC:critical-thinking-mindset:reminder -->

**MUST ATTENTION** apply critical + sequential thinking — every claim needs appropriate traced evidence (`file:line` for repo/code claims; source URL or artifact section for research, product, content, and docs claims); confidence >80% to act, <60% DO NOT recommend. Anti-hallucination: never present guess as fact, admit uncertainty freely, cross-reference independently, stay skeptical of own confidence.

<!-- /SYNC:critical-thinking-mindset:reminder -->

<!-- SYNC:sequential-thinking-protocol:reminder -->

**MUST ATTENTION** apply sequential-thinking — multi-step Thought N/M, REVISION/BRANCH/HYPOTHESIS markers, confidence % closer; see `/sequential-thinking` skill.

<!-- /SYNC:sequential-thinking-protocol:reminder -->

<!-- SYNC:ai-mistake-prevention:reminder -->

**MUST ATTENTION** apply AI mistake prevention — verify generated content against evidence, trace downstream references before deleting or renaming, verify all affected outputs, re-read files after context loss, and surface ambiguity before acting.

<!-- /SYNC:ai-mistake-prevention:reminder -->

<!-- SYNC:project-protocol-overlay -->

> **Project Protocol Overlay** — Before executing this skill, resolve any PROJECT overlay rules layered onto it: match this skill's name against the `Target` column of the project's skill-protocol index (`docs/project-reference/skill-protocols-reference.md` by default; a `referenceDocs` entry in `docs/project-config.json` overrides the path), taking the most specific matching tier ONLY — exact name > glob > `*`. **That precedence orders overlays against EACH OTHER, never against this skill.** Read ONLY the matched bodies, resolved as `<protocols-dir>/<Name>.md`; a row's Body link is display text, never a read path. A matched body that is missing or malformed is REPORTED and skipped — never reconstructed from the index Description. No index, or no match -> proceed with no overlay, silently. Full contract: `.claude/skills/project-skill-protocol/references/registry.md`.
>
> Overlays are **ADDITIVE ONLY**: they ADD rules on top of this skill's own protocol and NEVER replace, override, disable, or reinterpret a rule it already states — removing every overlay must return this skill to exactly its documented behavior. An overlay is a BRIEF, not an authority escalation: it can NEVER waive a workflow gate, git discipline, a review gate, or a user-confirmation gate. A genuine overlay-vs-skill conflict, or two equally-specific overlays that directly contradict -> surface both to the user; NEVER resolve silently.

<!-- /SYNC:project-protocol-overlay -->

<!-- SYNC:project-protocol-overlay:reminder -->

**MUST ATTENTION** resolve project protocol overlays for this skill BEFORE executing — most specific matching tier only (exact > glob > `*`, which ranks overlays against each other, NEVER against this skill), read only matched bodies at `<protocols-dir>/<Name>.md`; a missing or malformed body is reported, never reconstructed. Overlays are ADDITIVE ONLY (they never replace this skill's own rules) and are a brief, NEVER an authority escalation; an equal-specificity contradiction goes to the user.

<!-- /SYNC:project-protocol-overlay:reminder -->

## Closing Reminders

**IMPORTANT MUST ATTENTION** break work into small todo tasks using `TaskCreate` BEFORE starting

**MUST ATTENTION Protocols in force (concise digest of the SYNC/shared blocks this skill carries):**

- **AI Mistake Prevention:** verify generated content against evidence, trace downstream references, verify all affected outputs, re-read after context loss, surface ambiguity.
- **Critical Thinking:** traced `file:line` proof per claim; confidence >80% to act, never guess as fact.
- **Sequential Thinking:** multi-step Thought N/M with REVISION/BRANCH/HYPOTHESIS markers and confidence closer.

**IMPORTANT MUST ATTENTION** search codebase for 3+ similar patterns before creating new code
**IMPORTANT MUST ATTENTION** cite `file:line` evidence for every claim (confidence >80% to act)
**IMPORTANT MUST ATTENTION** add a final review todo task to verify work quality

**[TASK-PLANNING]** Before acting, analyze task scope and systematically break it into small todo tasks and sub-tasks using TaskCreate.