Change for a Dollar
Date: 14 Mar 1995 11:00:30 -0500 From: Anonymous Subject: Math How many different ways can you give change for a dollar? Is there a formula? Thanks.
Date: 27 Mar 1995 13:08:36 -0500 From: Dr. Sydney Subject: Re: Math Hello! You ask a good question, and I think you will find it fun to think about, so instead of giving you the answer, I am going to suggest how you might find the answer. One way to approach a problem like this is to deal with cases. By that, I mean that you should figure out how many possible cases there are in a systematic way. So, let's start with the biggest change we have. For $1, we can give 2 half dollars. That is case 1. Or, we could separate one of those half dollars, say into 2 quarters (Next you would say 5 dimes, then you would say 10 nickels, then 50 pennies, then figure out what all the combinations of pennies, nickels and dimes would give you 50 cents, and test those). We could then separate one of those quarters into 2 dimes and a nickel, or 5 nickels, ..... and so on. Do you see how you might go about figuring this out? It would take a long time and it would be best to write it out in some kind of organized chart, I think. Unfortunately , I don't know of a nice formula for figuring out how many ways there are to give change for a dollar. Another way you could approach this problem is to think of it in terms of the number 5. Here is what I mean....For the moment ignore the existence of pennies. Then, all you have to deal with are nickels, dimes, quarters, and half-dollars, right? Well, you could figure out what are the different combos of 5's that produce 100, and then figure out for each combo of fives what change will work (when doing this, take into account the existence of pennies again!). For instance, 5*2 + 5*3 + 5*15 = 100, so for the first 5*2 we could have a dime or 2 nickels or 10 pennies or 5 pennies and a nickel. Figure out the possiblities for the 5*3 and the 5*15, and then write down all the possible combinations of these combinations. Do this for all combos of 5's you can think of, and you should have a list of all possible ways you can give change for a dollar (be careful though, duplication will happen!). I hope this helps you get an idea of how to approach the problem. If you are confused by anything, write back and we'll try to clear it up! --Sydney, "Dr. Math"
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