problem-solving

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:

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

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[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.

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AI Mistake Prevention — Failure modes to avoid on every task:

Check downstream references before deleting. Deleting components causes documentation and code staleness cascades. Map all referencing files before removal. Verify AI-generated content against actual code. AI hallucinates APIs, class names, and method signatures. Always grep to confirm existence before documenting or referencing. Trace full dependency chain after edits. Changing a definition misses downstream variables and consumers derived from it. Always trace the full chain. Trace ALL code paths when verifying correctness. Confirming code exists is not confirming it executes. Always trace early exits, error branches, and conditional skips — not just happy path. When debugging, ask "whose responsibility?" before fixing. Trace whether bug is in caller (wrong data) or callee (wrong handling). Fix at responsible layer — never patch symptom site. Assume existing values are intentional — ask WHY before changing. Before changing any constant, limit, flag, or pattern: read comments, check git blame, examine surrounding code. Verify ALL affected outputs, not just the first. Changes touching multiple stacks require verifying EVERY output. One green check is not all green checks. Holistic-first debugging — resist nearest-attention trap. When investigating any failure, list EVERY precondition first (config, env vars, DB names, endpoints, DI registrations, data preconditions), then verify each against evidence before forming any code-layer hypothesis. Surgical changes — apply the diff test. Bug fix: every changed line must trace directly to the bug. Don't restyle or improve adjacent code. Enhancement task: implement improvements AND announce them explicitly. Surface ambiguity before coding — don't pick silently. If request has multiple interpretations, present each with effort estimate and ask. Never assume all-records, file-based, or more complex path.

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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.

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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, debug, architecture), advanced techniques (spiral refinement, hypothesis testing, convergence), and meta-strategies (uncertainty handling, revision cascades).

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MUST ATTENTION apply critical thinking — every claim needs traced proof, confidence >80% to act. Anti-hallucination: never present guess as fact.

<!-- /​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 — holistic-first debugging, fix at responsible layer, surface ambiguity before coding, re-read files after compaction.

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

Closing Reminders

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