Combinatorics
📋 What it is
Combinatorics counts how many arrangements or combinations are possible — like how many codes a lock has.
🗣️ Coach says
How many 3-digit codes can a lock have? Each digit has 10 choices, so 10×10×10 = 1000. Combinatorics is the maths of counting possibilities. It tells you how hard a lock is to brute-force — and sometimes reveals a shortcut.
🧠 Memory hook
Multiply the choices at each step to count the possibilities.
😂 Giggle
What did the player say after finally solving a hard logic puzzle?
"Well, that was logi-cool!"
😲 Whoa!
A standard bike combination lock with 4 dials of 10 digits has 10,000 codes — which is why patiently trying them all (brute force) can actually work if you have time.
✅ Quick check: A lock has 2 dials, each 0–9. How many codes are possible?
Say your answer out loud first — then reveal.
100 — 10 choices × 10 choices = 100 (00 through 99).
Multiply the number of choices at each independent position.
🪄 Trick question: Does adding one more 0–9 dial ADD 10 codes to a lock?
Careful — think it through, then reveal.
No — it MULTIPLIES by 10 (100 → 1000); each new dial multiplies, not adds, the possibilities.
Independent choices multiply, so possibilities grow explosively.
🧪 Try it! (2 minutes)
Count the outfits from 3 shirts and 2 pants (multiply!). Then add a hat choice — how many now?