Quandaries and Queries


I have 5 coins: a penny, a nickel, a dime, a quarter, and a loonie. How many different amounts of money could I pay using any combination of these coins? I don't want just the answer but the formula for working it out.

Grade 5 student



Hi Blaine,

You have 5 coins, each of a different value. If you are going to pay then, for each coin you have a decision to make. Do you include it or not. There are two choices for each coin.

Start with the penny, you have 2 choices.

Next the nickle. No matter which choice you made for the penny you have two possible choices for the nickle. Thus at this point you have 4 possible amounts,

  1. a penny and a nickle,

  2. a penny and no nickle,

  3. no penny and a nickle and

  4. no penny and no nickle.

Now the dime. From each of the 4 possible amounts above you get 2 amounts, you either include the dime or you don't include the dime. Hence with the three coins, penny, nickle and dime there are 23 = 8 possible amounts.

Can you finish the problem?

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