Piece Work

Mathematician Henri Picciotto was visiting a local McDonald’s with his son when he noticed that Chicken McNuggets are served in boxes of 6, 9, and 20 nuggets. This means that you can easily buy, say, exactly 15 nuggets, but not 16. What’s the largest “non-McNugget” number?

He worked it out on a napkin: It’s 43. If you want any number of Chicken McNuggets larger than 43, you can get them by buying some combination of 6-, 9-, and 20-nugget boxes. But if you want exactly 43, you’re out of luck.

(That was in the 1980s. Today you can buy 4 McNuggets in a Happy Meal, which simplifies the problem. Perhaps McDonald’s was listening.)