Frobenius Numbers

a pile of coins of different denominations

A World Without Ones invites you to consider what values can be made with just 3p and 7p coins. 

What can you discover about the values that can be made in a currency system with just two coin values?

Choose values for your two coins. You could pick 4p and 11p, or 5p and 7p, or 3p and 8p, or 6p and 15p, or...

For each pair of coin values, explore which totals can and can't be made.

Are there any pairs of coins where there are infinitely many values that can't be made?

Is there a quick way to work out the point after which every value can be made? (This is known as the Frobenius Number.)


 Share your thoughts and discoveries


If you could choose 3 coin values instead of just 2, the problem becomes much harder to solve. In fact, some aspects of this problem are still open and unsolved! This is called the Frobenius Coin Problem.