Make a List #6

ML #6

Hints and answers

At McDonald's, Chicken McNuggets come in boxes of 6, 9, and 20. What is the largest number of McNuggets you can't buy?


This is an unusual question, because it's about impossibility rather than possibility.

The most reasonable way to go about figuring out the answer is to make a list of possibilities. For instance, you can buy 6 McNuggets (of course), but you can't buy 7 or 8. You can buy 9, but not 10 or 11. A little farther along in the list, you will find that you can buy 24 McNuggets (24=9+9+6) but not 25, and then you can buy 26 (=20+6) And so forth.

Before you go too far, think about how you will know when you've gone far enough. The answer to this problem is larger than you might think at first!

Another strategy might be to do a simpler problem first -- try a situation where you can by 5 or 8 McNuggets, for example.

As always, be sure to explain the work you did to arrive at your answers!