A restaurant sells Chicken Nuggets in boxes of 6, 9, or 20. Obviously one could purchase exactly 15 Nuggets by buying a box of 6 and a box of 9.

Using only combinations of boxes of 6, 9, and/or 20 Nuggets:
a. Could you purchase exactly 17 Nuggets?
b. How would you purchase exactly 53 Nuggets?
c. What is the largest number for which it is impossible to purchase exactly that number of Nuggets?
d. Let’s say you could only buy the Nuggets in boxes of 7, 11, and 17. What is the largest number for which it is impossible to purchase exactly that number of Nuggets?