I am dealing with sets of problems that go as such: "How many n-cent postages can be formed from x and y cent stamps" For instance, I am doing a problem where x and y are 4 and 11 respectively. I don't understand how to determine a base case. I know that I must proof P(k + 1) for all P(i). The answer in my book is that the base case is a postage equal to 30 cents, but I don't follow. Could someone explain how I would go about finding a base case? The book seems to set this bound after showing 4 and 11 cent combinations up to 28. However, I do not see why 30 was chosen as a lower bound. Thanks.