Sorry Ya'll... Another Grad School Post!
Here is the scenario ...
McDonald's sells chicken nuggets in boxes of 6, 9, or 20. Obviously one could purchase exactly 15 nuggets by buying a box of 6 and a box of 9. Using only combinations of boxes of 6, 9, and/or 20 nuggets:
1) Could you purchase exactly 17 nuggets?
2) How would you purchase exactly 53 nuggets?
3) What is the largest number for which it is impossible to purchase exactly that number of nuggets?
4) Let's say you could only buy the nuggets in boxes of 7, 11, or 17. What is the largest number for which it is impossible to purchase exactly that number of nuggets?
#1: I could not come up with a way to purchase 17 nuggets. You could by 20 and throw 3 away, or you could purchase 3 boxes of 6 and throw 1 away. Purchasing just 17 is not possible.
#2: To purchase 53 nuggets you could purchase 1 box of 20, 1 box of 9, and 4 boxes of 6.
1 box of 20, 3 boxes of 9, and 1 box of 6.
#3: The largest number that cannot be purchased is 43. I used excel to list all the multiples of 6, 9, and 20 and then combinations of numbers. I then put the numbers in order from least to greatest, eliminated the duplicates and found that 43 is the largest number not listed.
#4: I solved this problem in the same manner. Using excel, I came up with 54 being the greatest number that you could to purchase exactly.