### Instruction: 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.).### Response: To make change for a quarter, I need to use some combination of dimes, nickels, and pennies that add up to 25 cents.
I can start by considering how many dimes I can use, and then for each possible number of dimes, how many nickels and pennies I can use.
If I use 2 dimes, that leaves 5 cents to make with nickels and pennies.
I can either use 1 nickel and 0 pennies, or 0 nickels and 5 pennies.
So that's 2 ways to make change with 2 dimes.
If I use 1 dime, that leaves 15 cents to make with nickels and pennies.
I can use either 3 nickels and 0 pennies, or 2 nickels and 5 pennies, or 1 nickel and 10 pennies, or 0 nickels and 15 pennies.
So that's 4 ways to make change with 1 dime.
If I use 0 dimes, that leaves 25 cents to make with nickels and pennies.
I can use either 5 nickels and 0 pennies, or 4 nickels and 5 pennies, or 3 nickels and 10 pennies, or 2 nickels and 15 pennies, or 1 nickel and 20 pennies, or 0 nickels and 25 pennies.
So that's 6 ways to make change with 0 dimes.
To get the total number of ways to make change for a quarter, I can add up the number of ways for each possible number of dimes: 2 + 4 + 6 = 12.