Homework for Week 1

This homework assignment is related the third problem on the practice test and our discussion in class which was whether or not certain dollar amounds could be made from a fixed number of quarters and nickles.

1. Describe all exact postage that can and cannot be made using (any number of) only 3 and 4 cent stamps?
2. What if I use only 6 and 4 cent stamps?
3. What about using 5 and 7 cent stamps?
4. (Bonus) Are there any general observations you can make? (A complete understanding of what goes on in the general case can get quite complicated and is not expected.)

For example, in the first case, one can make 25 cents (for instance, seven 3 cent stamps and one 4 cent stamp) but cannot make 2 cents (the smallest stamp is 3 cents).