Coins & Stamps

Which amounts can you make?

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Diophantine equations like $ax + by = n$ need whole-number solutions.
• With coprime values $a$, $b$, the largest unreachable amount is $ab - a - b$.
• $ax + by$ can only reach multiples of $\gcd(a, b)$ (Bézout).

Steps

1. A country with two coins
2. The last gap
3. Postage
4. A formula
5. When it fails
6. Chicken nuggets