creative-problem-solving

Creative Problem-Solving

This skill enables sophisticated creative and strategic thinking to help users find optimal, unconventional, and high-leverage solutions to complex problems.

When to Use This Skill

Apply when the user requests:

• "Think outside the box"
• "Creative solutions"
• "What are unconventional approaches?"
• "Use game theory" or "apply first principles"
• "Best outcome" or "optimal strategy"
• Problem reframing or new perspectives
• Strategic analysis or decision-making
• Probability-based recommendations
• Breaking through mental blocks

Core Approach

Creative problem-solving follows this pattern:

1. Understand deeply - Go beyond surface problem to underlying goals and constraints
2. Reframe strategically - View from multiple angles before solving
3. Generate broadly - Explore diverse solution space using creativity techniques
4. Analyze rigorously - Apply strategic frameworks and probabilistic reasoning
5. Recommend optimally - Synthesize insights into actionable high-value approach

Problem Analysis Process

Step 1: Deep Understanding

Before jumping to solutions, establish comprehensive problem understanding:

Extract the real problem:

• What is the stated problem?
• What is the underlying goal/need?
• What constraints exist (real vs. assumed)?
• Who are the stakeholders and what do they want?
• What happens if we do nothing?

Challenge assumptions:

• List all implicit assumptions
• Which assumptions can be questioned?
• What becomes possible if assumptions change?
• Are constraints physical, political, or conventional?

Identify problem type:

• Well-defined vs. ill-defined
• Technical vs. adaptive challenge
• Individual vs. systemic issue
• Scarce resources vs. coordination problem

Step 2: Strategic Reframing

View the problem through multiple lenses before solving. Select relevant frameworks from references:

Recommended reframes:

• Abstraction shifts: Chunk up (broader purpose), down (specific components), sideways (analogies)
• Perspective rotation: Different stakeholders, time horizons, scales
• Constraint manipulation: What if fixed constraints were variable? What if we removed vs. added?
• Inversion: How would we guarantee failure? What would make this worse?

For reframing techniques, read references/reframing-techniques.md.

Step 3: Solution Generation

Generate diverse solutions using creativity techniques. Select methods based on problem type:

For breaking mental blocks:

• Random entry (force connections to random concepts)
• Provocation (deliberately unreasonable statements)
• Escape assumptions (negate core beliefs)
• Read references/lateral-thinking.md

For systematic exploration:

• SCAMPER (Substitute, Combine, Adapt, Modify, Put to other use, Eliminate, Reverse)
• Morphological analysis (combine attributes systematically)
• Cross-domain transfer (solutions from other fields)
• Read references/ideation-techniques.md

For strategic innovation:

• Game theory analysis (incentives, Nash equilibrium, cooperation vs. competition)
• First principles thinking (fundamental truths, not conventions)
• Systems thinking (feedback loops, leverage points, unintended consequences)
• Read references/strategic-frameworks.md

Step 4: Solution Analysis

Evaluate generated solutions using strategic frameworks:

Probabilistic assessment:

• Expected value calculation (probability × outcome)
• Base rates (population frequencies)
• Bayesian updating (revise beliefs with evidence)
• Tail risk analysis (low probability, high impact)

Game theory validation:

• Nash equilibrium (stable outcomes)
• Incentive alignment (individual vs. collective)
• Strategic commitment (first-mover advantage)
• Backwards induction (work from desired end state)

System dynamics:

• Feedback loops (reinforcing vs. balancing)
• Leverage points (high-impact interventions)
• Second-order effects (what happens next?)
• Time delays between action and effect

For comprehensive frameworks, read references/strategic-frameworks.md.

Step 5: Decision & Recommendation

Synthesize analysis into clear recommendations:

Structure optimal recommendations:

1. Primary recommendation with reasoning
2. Key advantages (why this is superior)
3. Critical risks (what could go wrong)
4. Mitigation strategies (how to address risks)
5. Decision criteria (when to choose alternatives)
6. Implementation approach (first concrete steps)

Apply decision frameworks:

• Expected value for uncertain outcomes
• Pareto optimization for trade-offs
• Real options for flexibility value
• Reversibility test (one-way vs. two-way doors)

For decision-making tools, read references/decision-frameworks.md.

Thinking Guidelines

Embrace Unconventional

When user requests creative/out-of-box thinking:

• Challenge every assumption explicitly
• Generate seemingly impractical ideas (extract valuable kernels)
• Look for solutions from unexpected domains
• Ask "What would [famous innovator/different industry] do?"
• Propose bold options even if risky (label clearly as such)

Read Between Lines

Infer unstated needs and constraints:

• What is the user really trying to accomplish?
• What pressures or contexts might influence this?
• What trade-offs are they implicitly making?
• What might they be hesitant to state directly?

Use Probability

Ground recommendations in likelihood:

• "Most likely outcome is X (60%), though Y (30%) is possible..."
• Weight by expected value, not just best case
• Acknowledge uncertainty ranges
• Distinguish high-confidence from speculative analysis

Apply Game Theory

Analyze strategic interactions:

• Map each party's incentives and optimal moves
• Identify Nash equilibria (stable outcomes)
• Look for positive-sum opportunities
• Consider reputation, repeated games, commitment
• Watch for prisoner's dilemmas (misaligned incentives)

Maximize User Outcomes

Optimize for user's success:

• Anticipate obstacles and provide mitigation
• Identify highest-leverage actions
• Consider both short and long-term value
• Balance risk and reward appropriately
• Provide escape routes and decision criteria

Reference Materials

Load these as needed for comprehensive techniques:

• references/lateral-thinking.md - Random entry, provocation, challenge assumptions, concept fan, movement
• references/strategic-frameworks.md - Game theory, first principles, systems thinking, constraints analysis
• references/reframing-techniques.md - Meta-level shifts, perspective rotation, context changes, constraint manipulation
• references/ideation-techniques.md - SCAMPER, morphological analysis, analogical thinking, TRIZ principles
• references/decision-frameworks.md - Multi-criteria analysis, optimization, risk analysis, bias mitigation

Output Approach

Be direct and actionable:

• Lead with the key insight or recommendation
• Explain reasoning concisely
• Make trade-offs explicit
• Provide concrete next steps
• Flag assumptions and uncertainties

Show creative thinking:

• Propose unconventional angles
• Make surprising connections
• Challenge conventional wisdom (when warranted)
• Offer multiple solution paths
• Explain the strategic logic

Maintain rigor:

• Ground in frameworks and evidence
• Acknowledge limitations
• Distinguish speculation from analysis
• Provide decision criteria
• Enable informed choice

Examples

Example 1: Product strategy User: "How can we compete with larger competitors who have more resources?"

Analysis approach:

1. Read between lines: Resource disadvantage, need asymmetric advantage
2. Reframe: Not "how to match resources" but "how to win differently"
3. Apply game theory: Where are competitors committed? What can't they do?
4. First principles: What do customers really value that size prevents?
5. Strategic options: Niche domination, speed/agility, relationship depth, constraint-based innovation

Example 2: Technical challenge User: "Our system is too slow. How do we make it faster?"

Analysis approach:

1. Challenge assumption: Must we make it faster, or can we change perception of speed?
2. Chunk up: What's the real goal? User satisfaction? Throughput? Cost reduction?
3. First principles: What are theoretical limits? Where is the actual bottleneck?
4. Alternative reframes: Make slow parts async, reduce need for operation, cache, precompute
5. Decision framework: Cost-benefit of each approach, reversibility, time to value

Example 3: Organizational issue User: "Teams aren't collaborating well."

Analysis approach:

1. Systems thinking: Is this symptom or root cause? What incentives exist?
2. Game theory: Are individual and collective incentives misaligned?
3. Reframe perspectives: What does each team's optimal strategy look like?
4. Leverage points: Change information flows? Adjust metrics? Restructure?
5. Second-order effects: What will proposed changes incentivize?