How Many Combinations of Quarters, Dimes and Nickels Could Be Used to Pay 50 Cents in Change?

Robert Couse-Baker/CC-BY-2.0

There are 10 combinations of quarters, dimes and nickels that can be used to pay 50 cents in change. Each combination uses different quantities of each coin.

The possible combinations include 2 quarters; 5 dimes; 1 nickel, 2 dimes and 1 quarter; 2 nickels and 4 dimes; 3 nickels, 1 dime and 1 quarter; 4 nickels and 3 dimes; 5 nickels and 1 quarter; 6 nickels and 2 dimes; 8 nickels and 1 dime; and 10 nickels.

When including pennies, there are 49 possible combinations of coins that make up 50 cents in change. When including the half dollar, there are 50 combinations.

The United States Mint first produced coins in 1792. Coins were initially comprised entirely of silver until the silver value exceeded the coins’ face values in the 1960s. In 1965, a composite of nickel and copper layers was used to produce coins, except for the Kennedy half dollar, which still used silver but in a reduced quantity. The half dollar had popularity in the early 20th century and had strong use in casinos, where it remained popular for games that required 50-cent antes. As of 2014, four mints produce coins in the United States, with the main mint located in Philadelphia.