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 McNuggests?
Note: A formal mathematical approach to this problem might use number theory concepts to examine the Linear Combination 6a + 9b + 20c. A more informal approach would probably be appropriate for middle school or high school students.