ak-problem-solving

name	ak:problem-solving
description	Apply systematic problem-solving techniques when stuck. Use for complexity spirals, innovation blocks, recurring patterns, assumption constraints, simplification cascades, scale uncertainty.
user-invocable	true
when_to_use	Invoke when stuck and needing structured reframing.
category	utilities
keywords	["problem-solving","stuck","patterns","simplify"]
argument-hint	[problem description]
metadata	{"author":"agentkit","version":"2.0.0"}

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