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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