How Many Stamps Do You Need?

In this puzzle we ask you to figure out how best to put stamps on different packages.

In Seedonia you can mail a letter for 8 Seedos. (The Seedo is the unit of currency in Seedonia). Packages can cost any amount from 8 Seedos up depending on the size, weight, and destination.

A merchant has many different kinds of items to ship, so he knows he will need stamps of different denominations in order to total up to all the possible amounts he will need. He could get just 1-Seedo stamps, but that would require a great many stamps on some packages.

He finally figured out a way to do it with only two different denominations. What two stamp values did he use?

Course:

Math [1]

Result/Solution(s)

Stamp

The merchant bought 3-Seedo and 5-Seedo stamps. He proved to himself that he could put together combinations of these two denominations to equal any postage amount required in Seedonia.

Here is his proof:

The minimum postage in Seedonia is 8 Seedos, which can be made with a 5-Seedo stamp and a 3-Seedo stamp.
For any postage amount greater than 8, there are two possibilities:
- It includes a 5-Seedo stamp, or if it doesn’t,
- it includes at least three 3-Seedo stamps.
  - If it includes a 5, he can replace it with two 3s to get the next highest amount.
  - If it includes three 3s, he can replace them with two 5s to get the next highest amount.

In all cases where the postage is at least 8 Seedos, the next highest amount can be made by using one of these two replacements. So it is possible to reach any amount of 8 or more using just 3s and 5s.

Can you come up with other combinations that will work?

combination problems [2]