How Many Ways Can You Make 50 Cents With Coins?


Challenging students or friends to figure out how many different ways coins can be used to total 50 cents exercises their math and number proficiency, but it also helps develop problem-solving and reasoning skills. Before you set them to the task, you need to know that there are 50 different ways to use U.S. coins, if you include the half-dollar piece.

Considering the Combinations

  • Provide a hint to the solution by setting up a five-columned chart, with column headings of “Half-dollar,” “Quarter,” “Dime,” “Nickel” and “Penny.” Start by marking how many of each coin you would use if you were adding no others. For example, you would mark one under the first column, two for quarters, five for dimes, 10 for nickels and 50 for pennies. Next, calculate the combinations for one quarter and other coin choices: one quarter, two dimes and a nickel; one quarter, two dimes and five pennies; one quarter, one dime and three nickels; and so on. Continue by dropping one more of the largest coin until you’ve found all of the combinations. Count them up, and you’ll find 49 combinations plus the half-dollar choice.

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