Famous Problems & Puzzles
📋 What it is
Classic problems (bridges, four colours, impossible constructions) show how proof settles what looks unsolvable.
🗣️ Coach says
The greatest puzzles in history weren’t solved by guessing — they were SETTLED by proof. Some were proven possible, some proven impossible. Either way, a proof turns “I wonder…” into “now we know for sure.”
🧠 Memory hook
A proof can say “impossible” as firmly as “here’s how.” Both are real answers.
😂 Giggle
What did the biconditional say?
"If AND only if — I go both ways!"
😲 Whoa!
The Seven Bridges of Königsberg puzzle looked like a walking challenge — but Euler PROVED no such walk exists, and in doing so invented a whole branch of math (graph theory).
✅ Quick check: A puzzle is proven to have NO solution. Is that a failure to solve it?
Say your answer out loud first — then reveal.
No — proving no solution exists IS solving it; you now know the truth with certainty instead of guessing forever.
An impossibility proof is a complete, valuable answer, not a dead end.
🧪 Try it! (2 minutes)
Try to draw an envelope shape without lifting your pen or retracing. If you can’t, ask: could that be provably impossible? (Look up “Euler path”.)