Sue Pinion, Sandy McAdams, Lisa Stueve

### McDonalds sells Chicken McNuggets in boxes of 6, 9, or 20. Obviously one could purchase exactly 15 McNuggets by buying a box of 6 and a box of 9. Could you purchase exactly 17 McNuggets? How would you purchase exactly 53 McNuggets? What is the largest number for which it is impossible to purchase exactly that number of McNuggets? What if the McNuggets were available in boxes of 7,11, and 17? What is the largest number for which it is impossible to purchase exactly that number of McNuggets?

In the first case, it is impossible to purchase 17 nuggets. Yet, 53 nuggets can be purchased by buying a box of 20 , 3 boxes of 9, and 1 box of 6. After working the problem out with paper and pencil, it appears that every number after 43 can be generated in the 6,9,20 version of the problem. We believe that every number after 37 can be generated in the 7, 11, 17 version of the problem. This combination was obtained by using a spreadsheet. It is almost impossible to create every possibility on the spreadsheet. Therefore we created a basic spreadsheet using all the basic possiblilities for combinations which we copied and pasted when trying to calculate the total possible sums. The first column of the spreadsheet can be changed from 0 to 1 to 2, etc. in order to get all the possiblities. Then the spreadsheet was sorted for number after they were multiplied by the appropriate values of nuggets.
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