Math CentralQuandaries & Queries


Question from Elizabeth, a student:

At a hamburger stand you can order a hamburger with any of the following, in any combination: ketchup, mustard, pickles, onions, tomatoes, mayonnaise and/or lettuce. How many different hamburgers is it possible to order?

Hi Elizabeth,

You stand at the window and the server says

Do you want Ketchup?

You answer yes or no.

Do you want mustard?

You answer yes or no.

and so on through the list of 7 possible toppings. Each time you have 2 different answers so that's

2 × 2 × 2 × 2 × 2 × 2 × 2 = 27

possible hamburgers.

If this is the school cafeteria and you choose a different hamburgers each school day how many weeks will it take until you have tried all the combinations?


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