Factoring in the Chicken McNugget Monoid

摘要

Every day, 34 million Chicken McNuggets are sold worldwide. At mostMcDonalds locations in the United States today, Chicken McNuggets are sold in packs of 4, 6, 10, 20, 40, and 50 pieces. However, shortly after their introduction in 1979, they were sold in packs of 6, 9, and 20. The use of these latter three numbers spawned the so-called Chicken McNugget problem, which asks: "What numbers of Chicken McNuggets can be ordered using only packs with 6, 9, or 20 pieces?" In this article, we present an accessible introduction to this problem, as well as several related questions whose motivation comes from the theory of nonunique factorization.