Discrete Math

Use the cashier's algorithm to make change using quarters, dimes, nickels, and pennies for

a$)87$ cents.

b$)49$ cents.

c$)99$ cents.

d$)33$ cents.

Use the cashier's algorithm to make change using quarters, dimes, nickels, and pennies for

a$)51$ cents.

b$)69$ cents.

c$)76$ cents.

d$)60$ cents.

Answer

Use the cashier's algorithm to make change using quarters, dimes, and pennies $($but no nickels$)$ for each of the amounts given in

Exercise $57.$ For which of these amounts does the greedy algorithm use the fewest coins of these denominations possible?

Cashier's algorithm uses fewest coins in parts $($a$),($c$),$ and $($d$).$

a$)$ Two quarters, one penny

b$)$ Two quarters, one dime, nine pennies

c$)$ Three quarters, one penny

d$)$ Two quarters, one dime

For Exercise $59,$ the last question is asking which of the greedy solutions is optimal in

the sense that the change cannot be done with fewer coins. One of them is suboptimal. Which one

is it$?$