Generalize the Rule
📋 What it is
After solving a specific case, ask “what’s the general rule?” — a formula that works for ANY numbers.
🗣️ Coach says
The deepest skill: after solving “handshakes for 5 people = 10,” find the RULE for any number (n people → n(n−1)/2). Generalizing turns one answer into a formula that solves every version forever.
🧠 Memory hook
Solve one case, then ask “what’s the rule for ANY number?” — that’s a formula.
😂 Giggle
Why was the number 25 so good at quarters?
Because four of them always make a whole 100!
😲 Whoa!
The handshake formula n(n−1)/2 also counts the lines between dots, the games in a round-robin tournament, and the pairs in a group — one rule, many problems.
✅ Quick check: Handshakes: 3 people = 3, 4 = 6, 5 = 10. What’s the rule for n people?
Say your answer out loud first — then reveal.
n(n−1)/2 — each of n people shakes (n−1) others, and each shake is counted twice, so divide by 2.
Generalizing the pattern into a formula solves every case at once.
🧪 Try it! (2 minutes)
You found 1, 3, 6, 10 for handshakes. Predict 6 people using the pattern, then check with n(n−1)/2.
🔎 How did you work this?