Question

How many ways can change be made for a quarter using standard u.s. coins? (don't count "1 quarter" as making change for a quarter.)?

Answer 1

25 pennies, 2 dimes and 5 pennies, 2 dimes and 1 nickel, 4 nickels.

Answer 2

There are 12 different ways to make change for a quarter without using a quarter itself.

A penny is worth 1 cent, a nickel is worth 5 cents, and a dime is worth 10 cents. With these values, the following combinations of coins will make change for a quarter, which is 25 cents:

Order: pennies, nickels, dimes

-
(1) 25 pennies

(2) 20 pennies, 1 nickel

(3) 15 pennies, 2 nickels
(4) 15 pennies, 1 dime

(5) 10 pennies, 3 nickels
(6) 10 pennies, 1 nickel, 1 dime

(7) 5 pennies, 4 nickels
(8) 5 pennies, 2 nickels, 1 dime
(9) 5 pennies, 2 dimes

(10) 5 nickels
(11) 3 nickels, 1 dime
(12) 1 nickel, 2 dimes