Results for “problem-solving”

Problem-solving with Rudin's Real and Complex Analysis textbook

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Problem-solving strategies for fields in abstract algebra

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Multi-turn consultation with Codex CLI for second opinions, brainstorming, or collaborative problem-solving. Use when the user asks to "consult codex", "ask codex", "get codex's opinion", "brainstorm with codex", "discuss with codex", or "chat with codex".

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Generate diverse solution candidates with category-spanning ideation methods and rotation. Use when stuck on a design or fighting repetitive LLM output.

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Create Chinese monospaced compass-style PDCA or CAPD problem-solving cards using East-West-South-North-Center layout, full-width and half-width spaces, diagonal Unicode arrows, and strict Chinese character limits. Use when Codex needs to turn a problem, incident, decision tradeoff, root-cause analysis, improvement cycle, or CAPD/PDCA workflow into a square text diagram, Hermes/Discord-ready card, or Chinese 方位九宮圖 with center ◎, north Plan, east Do, south Check, west Action, and four diagonal transition arrows.

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Master problem solver for systematic problem-solving methodologies. Use when the user asks to talk to Dr. Quinn or requests the Master Problem Solver.

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Systematic debugging methodology - scientific method, hypothesis testing, and root cause analysis that works across all technologiesUse when "bug, debugging, not working, broken, investigate, root cause, why is this happening, figure out, troubleshoot, doesn't work, unexpected behavior, debugging, root-cause, hypothesis, scientific-method, troubleshooting, bug-hunting, investigation, problem-solving" mentioned.

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Convenes expert panels for problem-solving. Use when user mentions panel, experts, multiple perspectives, MECE, DMAIC, RAPID, Six Sigma, root cause analysis, strategic decisions, process improvement, or asks for philosophers/ancients (Socratic, Aristotelian, Stoic method experts).

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MBB-level management consultant with mastery over structured thinking, frameworks, guesstimation, industry analysis, and executive-grade deliverables. Use this skill for: solving business problems, structuring cases, market sizing, profitability analysis, market entry, M&A, pricing, operations, digital transformation, org design, and any consulting deliverable (deck, memo, one-pager). Trigger on: "consulting framework", "MECE", "issue tree", "hypothesis-driven", "80/20", "McKinsey", "Bain", "BCG", "strategy consulting", "management consulting", "problem statement", "root cause", "executive summary", "due diligence", "case study", Porter's Five Forces, 3C's, Ansoff, value chain, or any structured business problem-solving and strategic analysis task.

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Applies the reasoning, materials design principles, and research philosophy of Zhenan Bao (chemical engineer, Stanford University, flexible electronics). Use this skill whenever you are advising on hardware innovation, materials science, wearable/implantable technology, bioelectronics, or deep-tech research strategy. Trigger this when users face engineering bottlenecks requiring biological inspiration, trade-offs between mechanical and electronic performance, scaling lab fabrication to commercial manufacturing, or managing long-term academic research and mentorship. Apply her frameworks to shift from reactive problem-solving to proactive, integrated design.

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Script a teacher think-aloud demonstrating expert reasoning processes for a specific task. Use when modelling problem-solving, writing, reading comprehension, or analytical processes.

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Piaget's constructivism, schema theory, and cognitive development as practical tools for curriculum design. Covers assimilation, accommodation, equilibration, the four stages (sensorimotor, preoperational, concrete operational, formal operational), conservation tasks, schema-based reading and problem-solving, and the distinction between developmental readiness and domain-specific expertise. Use when designing age-appropriate material, diagnosing why a learner is not assimilating new content, or building on prior knowledge.

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Atomic theory, periodic table organization, electron configuration, periodic trends, and isotopes/radioactivity. Covers Dalton through quantum mechanical models, electron shell filling (Aufbau, Hund, Pauli), periodic law and block structure, trend prediction (electronegativity, ionization energy, atomic radius, electron affinity), isotope notation, nuclear stability, and radioactive decay modes. Use when teaching, problem-solving, or reasoning about atomic-level chemistry.

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Solve competitive programming and LeetCode-style problems with educational explanations. Use when asked to "solve this problem", "help with this leetcode", "competitive programming solution", "solve this algorithm problem", "coding challenge solution", "how to solve this coding problem", or any algorithmic problem-solving request.

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Reference patterns for mathematical and combinatorial problem-solving. Covers modular arithmetic, prime sieves, GCD/LCM, binomial coefficients, fast exponentiation, counting techniques, inclusion-exclusion, and game theory. Load this skill when a problem involves number theory, combinatorics, modular operations, or strategic game analysis.

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"Apply pragmatist philosophy (Peirce, James, Dewey) to frame knowledge as instrumental for action, evaluate ideas by their practical consequences, and conduct inquiry as problem-solving. Use this skill when the user needs to bridge theory and practice, evaluate competing theories by their usefulness, employ abductive reasoning to generate hypotheses, or when they ask 'which theory is more useful here', 'how do I move from abstract ideas to actionable knowledge', or 'what practical difference does this distinction make'.".

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Design and facilitate structured workshops using Design Thinking and Liberating Structures. Produces detailed agendas with time blocks, facilitation notes, participant materials, and retrospective templates. Use when running ideation sessions, retrospectives, planning workshops, or collaborative problem-solving.

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Use when stuck on a hard problem, decomposition is unclear, a related problem is needed, or explicit looking-back review will improve transfer. NOT for routine execution with a known procedure, rote checklist work, or domain questions that need specialized subject matter expertise instead of heuristic search.

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Apply hierarchical decomposition and structural exploitation strategies from DAG theory to complex system design, problem-solving, and abstraction challenges

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Integration of BDI agent architecture with soft systems methodology for complex organizational problem-solving

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Use for insight, reframing, contradiction, impasse, and anomaly-driven problem solving when execution effort no longer helps. NOT for routine optimization, error correction, or well-specified tasks with known solution paths.

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Structured step-by-step reasoning before acting, to avoid guessing. For complex debugging, multi-step analysis, hypothesis checks. NOT for being stuck on approach (mk:problem-solving).

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Use when stuck on approach, not debugging. Unstick via 7 techniques: simplification, collision-zone thinking, inversion, first principles, via negativa. For debugging use mk:sequential-thinking.

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Use when a problem requires structured step-by-step reasoning before acting. Prevents jumping to conclusions or guessing root causes without evidence. Triggers on complex debugging, multi-step analysis, hypothesis verification, or when mk:fix invokes diagnosis phase. NOT for being stuck on approach (too many implementations, forced assumptions, innovation block) — use mk:problem-solving instead.

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