definition:
George Polya developed a systematic approach to problem-solving with four key steps:
- Understand the problem *What is the unknown? *What are the given data? *What are the conditions?
- Devise a plan *Look for patterns *Work backwards *Use analogies *Break into smaller problems
- Carry out the plan *Execute your strategy *Check each step *Be patient and persistent
- Look back *Check the result *Can you verify the answer? *Can you use this method elsewhere?
example:
Problem: At a party with 10 people, if everyone shakes hands with everyone else exactly once, how many handshakes occur?
- Step 1: Understand 🤔 Unknown: Total number of handshakes Given: 10 people, each shakes hands once with every other person Condition: No person shakes hands with themselves
- Step 2: Plan 📊 Strategy: Use combinations formula Each handshake involves exactly 2 people Choose 2 people from 10: C(10,2)
- Step 3: Execute 🔢
C(10,2) = 10!/(2!(10-2)!) = (10 × 9)/2 = 45 - Step 4: Verify ✨
- Check: Person 1 shakes 9 hands, Person 2 shakes 8 remaining, etc.
- Sum: 9+8+7+6+5+4+3+2+1 = 45 ✅
- Answer: 45 handshakes