Extension Problems for Postage Stamp Arithmetic
Here are a few extensions. There are undoubtedly many more good ones. Let us know if you have one that you like.
What about three denominations of stamps? For example, if you had 13-, 21- and 30-cent stamps, what is the largest amount that you cannot make?
If a country's currency consisted of 9-gauss and 16-gauss coins, what amounts may shopkeepers charge for their wares and still give exact change for purchases? How is this coinage problem different from the postage stamp problem?
In the Kingdom of Cantor, there are two stamp denominations: 1 georg and georgs. How many different postage amounts can you make with 100 1's and 100 's?