Number Reasoning
📋 What it is
Many puzzles hide number patterns — powers of two, GCDs, remainders — that reveal the answer or prove it impossible.
🗣️ Coach says
Behind the pegs and jugs, the same number ideas keep appearing: powers of two (Hanoi), GCD (water-pouring), remainders and parity (impossible scrambles). Spotting the number underneath turns a “try everything” puzzle into a “I know the rule” puzzle.
🧠 Memory hook
Look under the puzzle for the number rule — powers of 2, GCD, or remainders.
😂 Giggle
Why did the puzzler work backwards?
Because starting from the answer sometimes reveals the way!
😲 Whoa!
The same “remainder” idea (modular arithmetic) that solves clock puzzles and the water-jug puzzle also secures your online passwords — one number idea, everywhere.
✅ Quick check: Hanoi uses powers of two and water-pouring uses GCD. What does that tell you about puzzles?
Say your answer out loud first — then reveal.
That a hidden number rule often controls the puzzle — find the rule and you can predict or prove the answer instead of guessing.
Recognising the underlying number structure is the key meta-skill.
🧪 Try it! (2 minutes)
Take any puzzle you’ve met and ask: is there a number rule hiding in it (doubling? even/odd? remainders?)?