The Chicken McNugget Theorem, Explained

The BTS Chicken McNugget Meal, Why you can’t buy 43 McNuggets at McDonald’s, and a math problem from the 1800s.

Photo by Food Photographer David Fedulov on Unsplash

Throughout the past month, the BTS Chicken McNugget meal has been everywhere.

The collab between McDonald’s and K-Pop group BTS launched in the U.S. on May 26, 2021, and for a brief moment it felt like BTS and McNuggets were inseparable from each other. The BTS meal was sold out at nearly every McDonald’s. Artist Josiah Chua turned the packaging into these fire sneakers. And of course, there was that McNugget from the BTS meal that sold for nearly $100,000 on eBay because it looked like an Among Us character, which really makes me think McDonald’s should’ve shaped the BTS McNuggets to look like BTS. Can you imagine how much someone would pay for a McNugget that looks like Jungkook? Never underestimate how much people will pay for 1) food that looks like pop culture and 2) anything BTS-related.

The promotion is over now (at least in the U.S.), but there is still lots to learn about Chicken McNuggets. For example, it used to be mathematically impossible to order 43 McNuggets at any McDonald’s in the United Kingdom. Why? Because of a math theorem appropriately called the Chicken McNugget Theorem.

In honor of the BTS Chicken McNugget meal, I’m going to explain the Chicken McNugget Theorem and its proof. We’re going to go over:

• Where the Chicken McNugget Theorem Came From (hint: the 1800s)
• How to Prove the Chicken McNugget Theorem
• How to Apply the Chicken McNugget Theorem to the BTS Meal

Origin Story of the McNugget Theorem

In the United Kingdom, McDonald’s used to only sell Chicken McNuggets in packs of 6, 9 and 20 (and unfortunately, none of them looked like Jungkook). So of course, if you want 12 McNuggets, you can buy two packs of 6. On the other hand, you can’t buy 11 nuggets at a time if your only options are 6, 9 and 20: it’s impossible.

Mathematicians wanted to answer this question:

What is the largest number of McNuggets that you can’t buy with packs of 6, 9 and 20?