Water-Pouring & GCD
📋 What it is
Water-pouring puzzles (measure exactly N litres with two jugs) can ONLY reach amounts that are multiples of the jugs’ GCD.
🗣️ Coach says
With a 3-litre and 5-litre jug you can measure 4 litres — but never 4½. There’s a hidden law: you can only make multiples of the GCD (greatest common divisor) of the jug sizes. GCD(3,5)=1, so you can make ANY whole number.
🧠 Memory hook
You can only measure multiples of the GCD of the two jug sizes.
😂 Giggle
Why did the weighing puzzle love a balance scale?
Because it always knew which side to take!
😲 Whoa!
This exact puzzle appears in the movie Die Hard — and the “only multiples of the GCD” rule means some target amounts are flat-out impossible no matter how clever you are.
✅ Quick check: With a 4-litre and 6-litre jug, can you measure exactly 5 litres?
Say your answer out loud first — then reveal.
No — GCD(4,6) = 2, so you can only make even amounts (2, 4, 6…); 5 is odd, so it’s impossible.
Only multiples of the jugs’ GCD are reachable.
🪄 Trick question: Two jugs of 2 and 4 litres — can you measure 3 litres?
Careful — think it through, then reveal.
No — GCD(2,4) = 2, so only even amounts are possible; 3 can’t be made.
The GCD rule forbids amounts that aren’t its multiples.
🧪 Try it! (2 minutes)
With imaginary 3- and 5-litre jugs, find the steps to get exactly 4 litres. (Hint: fill, pour, empty.)