This is from Discrete Mathematics and its Applications.
Here is the book's section on the greedy alorithm for counting change
Here is the problem I am working on, 54(uses 52)
Here is what I got for 54
54a. d1 = 3 d2 = 1 d4 = 2
54b. d1 = 1 d2 = 2 d4 = 4
54c. d1 = 3 d2 = 2 d4 = 4
54d. d1 = 1 d2 = 0 d4 = 8
Where d1 - number of quarters, d2 - number of dimes, d4 - number of pennies. Can someone confirm my suspicions that for all of these amounts, the greedy algorithm will use the fewest coins possible because the number of pennies never gets to the amount that a nickel could replace, 5?