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. Thanks. 

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.
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 2^{3} = 8 possible amounts. Can you finish the problem?Penny 

