The Chicken McNugget Theorem
Written By: Ritvik Ranjan
In the world of mathematics, there exists many, many different theorems. The names of these theorems are typically chosen by their finders. Some of these names are representative of the ideas themselves, or their founders. However, some theorems have completely unique and unexpected names not traditionally associated with mathematics. In this series of articles by Science Rewired, we explore the weirdest-named math theorems out there, as well as what they do and how they work.
Now picture this: a group of hungry mathematicians, fueled by nothing but caffeine and a burning desire for truth, pondering the pressing question—how many Chicken McNuggets can you not buy at McDonald's? Yes, you heard that right. We're not here to calculate how many nuggets you can devour in one sitting (although that's a tempting thought). Instead, we're tackling the realm of impossibility—figuring out the largest number of McNuggets that cannot be purchased using only certain pack sizes.
Enter the Chicken McNugget Theorem. Despite its whimsical name, this theorem has a surprisingly strong mathematical foundation. It's not about the taste of those crispy, golden nuggets or the questionable nutritional value they offer; instead, it's a fascinating exploration into the world of number theory.
So, what exactly is the Chicken McNugget Theorem? Named after the famous McDonald's menu item, this theorem addresses a seemingly simple question: given two relatively prime positive integers m and n, what is the largest integer that cannot be expressed as a combination of m and n? In more digestible terms, if you can only buy Chicken McNuggets in packs of m and n, what's the largest number of nuggets you can't order?
Let's break it down with a hypothetical scenario. Imagine McDonald's only sells Chicken McNuggets in packs of 6 and 9. You might start by ordering 6 nuggets, then 12, then 18, and so on. You can also order 9 nuggets, 15, 21, and so forth. But what about numbers like 5, 7, or 11? These are impossible to reach using only packs of 6 and 9. The Chicken McNugget Theorem tells us that for packs of m and n, the largest number of nuggets you cannot order is mn-m-n. In this scenario, that is 9 x 6 – 9 – 6 = 39.
Now, you might wonder: why is this theorem called the Chicken McNugget Theorem? Well, it's a testament to the power of pop culture and the quirky creativity of mathematicians. Legend has it that mathematicians, while pondering this problem, found themselves in a McDonald's, staring at a menu board adorned with images of those iconic golden nuggets. With hunger gnawing at their stomachs and numbers swirling in their heads, they christened their discovery the "Chicken McNugget Theorem" in a nod to their surroundings.
But don't let the playful name fool you—this theorem has serious mathematical implications. It's not just about fast food; it's about exploring the fundamental properties of numbers and uncovering patterns that extend far beyond the realm of nugget cravings.
The beauty of the Chicken McNugget Theorem lies in its simplicity and universality. While it may have originated from a craving for fast food, its principles apply to a wide range of mathematical problems. From coin denominations to postage stamps, this theorem offers insights into countless real-world scenarios where we need to find the largest number that can't be formed by combining given quantities.
Moreover, the Chicken McNugget Theorem opens doors to deeper mathematical inquiries. Mathematicians have extended its concepts to higher dimensions, exploring similar problems in three dimensions and beyond.
So, the next time you find yourself munching on a box of Chicken McNuggets, take a moment to appreciate the mathematical marvel behind those crispy, golden bites. And remember, while the Chicken McNugget Theorem may have a quirky name, its mathematical versatility is anything but trivial.
Works Cited:
Art of Problem Solving. (n.d.).
https://artofproblemsolving.com/wiki/index.php/Chicken_McNugget_Theorem
Beneschan, M. (2023, November 27). The Chicken McNugget Theorem, Explained - Mike Beneschan - Medium. Medium. https://mikebeneschan.medium.com/the-chicken-mcnugget-theorem-explained-2daca6fbbe1e
Postage Stamp Problem / Chicken McNugget Theorem | Brilliant Math & Science Wiki. (n.d.). https://brilliant.org/wiki/postage-stamp-problem-chicken-mcnugget-theorem/
The Chicken McNugget Theorem. (2013, March 1). Puzzling Mathematics. https://tcmtan.wordpress.com/2013/01/19/the-chicken-mcnugget-theorem/
