$3.$ Consider the problem of making changes for n cents using the fewest number of coins. Assume that each coin's value is an integer. a$.$ Describe a greedy algorithm to make change consisting of quarters, dimes, nickels, and pen XL$18$ nies. b$.$ Suppose that the available coins are in the denominations that are powers of c$,$ i$.$e$.,$ the denominations are c$,$ c$\text{'},$ ck for some integers c$>1$ and k $>=1.$ Describe a greedy algorithm. c$.$ Give a set of coin denominations for which the greedy algorithm does not yield an optimal solution. Your set should include a penny so that there is a solution for every value of n$.$ You only need to give at least one example.