Amanda went to the store to purchase ink pens. She found three kinds of pens. The first cost $4 each; the price of the second kind was 4 for $1; and the cost for the third kind was 2 for $1. She bought 20 pens and she bought at least one of each kind. (It is possible to buy only 1 of the pens that are “4 for $1” or “2 for $1”.) The cost was $20. When she got back to her office, Amanda decided to turn this into a math problem for me. She asked: how many of each kind did I buy?