The Post Office down the road has run out of all stamps except 3c and 5c stamps. They have a large amount of each of these. What amounts of postage, up to $2 can the Post Office make with the stamps that they have left?
Solution:
Experimenting will tell you that the Post Office can make up the following small amounts: 3c, 5c, 6c, 8c, 9c and 10c.
Once we know that they can make up 8c, 9c and 10c we can see that they can do everything else up to $2. This is because they can keep adding 3c stamps like this:
| 8, | 8 + 3 = 11, | 8 + 3 + 3 = 14, | 14 + 3 = 17, | 17 + 3 = 20, ... |
| 9, | 9 + 3 = 12, | 9 + 3 + 3 = 15, | 15 + 3 = 18, | 18 + 3 = 21, ... |
| 10, | 10 + 3 = 13, | 10 + 3 + 3 = 16, | 16 + 3 = 19, | 19 + 3 = 22, ... |
Continually adding 3c stamps in this way will cover all the values from 8c up to 200c = $2
Extension
What amounts of postage can they make with 3c and 7c stamps?