Coin Combinations Quickened by Process of Elimination
Date: 11/04/2013 at 21:02:55 From: Albert Subject: What is an efficient way of solving this problem Dear Dr. Math, How many different amounts of money can be made from 4 pennies, 2 nickels, 1 dime, and 1 quarter if one or more coins can be used in each amount? I could not figure out what is a good way to tackle a problem like this. I tried listing all the possibilities and creating a tree diagram, but both of those approaches were confusing. ... and time-consuming: this problem is from a 1988 Olympiad, which allowed 3 minutes to work out the problem. Could you tell me a way that will work out in the allotted time? I would really appreciate a thorough response. Thank you.
Date: 11/05/2013 at 16:02:15 From: Doctor Greenie Subject: Re: What is an efficient way of solving this problem Hi, Albert -- (1) Find the total value of all the coins; that will give you the maximum possible answer; then (2) See if any of the total values less than the overall total can NOT be made. The total value of the coins is 49 cents; so the largest possible answer to the question is 49. Some quick analysis shows that you can make any total from 1 to 24 cents using the dime, nickels, and pennies. Then the quarter itself makes 25 cents; and adding the quarter to each of the combinations using the smaller coins will allow you to make any total from 26 to 49 cents. So there are no totals that you can NOT make using the given coins; and the number of different totals you can make is 49. - Doctor Greenie, The Math Forum http://mathforum.org/dr.math/
Date: 11/08/2013 at 13:57:47 From: Albert Subject: Thank you (What is an efficient way of solving this problem) Thanks, Dr. Greenie! That is an awesome solution.
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