## Postage Stamps

#### Problem

A small village post office is selling 1st class stamps and 2nd class stamps in a book costing £1. If a 1st class stamp is 9p and a 2nd class stamp is 7p, how many ways can a £1 book be filled?

#### Solution

We are attempting to solve the Diophantine equation 9`a` + 7`b` = 100, of which there are two positive solutions:

1 9 + 13 7 = 100

8 9 + 4 7 = 100

How many solutions are there to the equation 4`a` + 3`b` = 100?

Try different equations and see if you can spot any patterns.

Problem ID: 58 (Dec 2001) Difficulty: 1 Star