Design a greedy algorithm to make change for n cents using the least number of coins among quarters (25), dimes (10), nickels (5), and pennies (1). Fully explain your algorithm. For example, if n = 91, your algorithm must return 6, since we can make change for 91 cents using 6 coins: Take 3 quarters, 1 dime, 1 nickel, and 1 penny. Also, we can show that it is not possible to make change for 91 cents using less than 6 coins. (b) Show that your algorithm in part (a) outputs a correct result for all positive integers n.

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