🧠 Problem-Solving Tips

Heuristics, checklists, and strategies for solving AMC counting and probability problems efficiently.

📚 Tip Categories

🎯 Recognition Strategies

• Problem Type Identification: Quick cues to identify problem patterns
• Constraint Analysis: How to spot and handle different types of constraints
• Symmetry Detection: When and how to use symmetry principles

🔧 Solution Techniques

• Complement Counting: When to use “total - unwanted” approach
• Casework Discipline: How to organize and avoid overcounting
• Indicator Variables: Using linearity of expectation effectively

⚠️ Common Pitfalls

• Overcounting Alarms: Warning signs of double-counting
• Indistinguishable Items: When objects are the same vs. different
• Replacement Confusion: With vs. without replacement scenarios

🏆 Contest Strategy

• Time Management: How to allocate time effectively
• Problem Prioritization: Which problems to tackle first
• Answer Verification: Quick sanity checks for your solutions

🎯 How to Use This Section

1. Before Practice: Review the recognition strategies
2. During Practice: Use the solution techniques
3. After Practice: Check against the common pitfalls
4. Contest Day: Apply the contest strategy

📊 Tip Priority by Level

AMC 10 Essential

• Basic recognition strategies
• Simple solution techniques
• Common pitfall avoidance
• Time management basics

AMC 12 Essential

• Advanced recognition strategies
• Complex solution techniques
• Advanced pitfall avoidance
• Sophisticated contest strategy

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