Chicken McNugget Theorem
The Chicken McNugget Theorem is a mathematical theorem from number theory that I chose as my final project presentation topic for CMSC398L: Competitive Programming. It is also known as the Frobenius Coin Theorem, and it is used to find the largest integer that cannot be expressed in the form am + bn, where a and b are relatively prime positive integers. In my presentation, I introduced the theorem through a football scoring example using 3-point field goals and 7-point touchdowns. This made the abstract idea easier to understand before connecting it to the formula ab - (a + b).
This artifact is important because it represents my love for problem solving and mathematics. One of the reasons I became more interested in math during college is that I enjoy the process of taking a problem that looks simple at first and discovering the deeper structure behind it. The Chicken McNugget Theorem is a good example of that. The question itself seems almost playful, but solving it requires mathematical reasoning, pattern recognition, and an understanding of why certain numbers can or cannot be formed. That kind of problem is exactly what draws me to mathematics because it rewards curiosity, patience, and logical thinking.
This project also connects to my interest in computer science because competitive programming often depends on recognizing the mathematical idea behind a problem before writing any code. The coding implementation of the theorem is very simple, but the real value comes from understanding why the formula works and when it can be applied. This helped me see how mathematics and programming support each other.
The presentation also helped me develop my technical writing and communication skills. Since the theorem can be abstract for someone seeing it for the first time, I had to think about how to explain it in a clear and accessible way. Instead of starting with only the formula, I used a familiar example and then built towards the general rule. This made the presentation more effective because it focused not just on what the theorem says, but on helping the audience understand why it matters.
Overall, this artifact shows my ability to communicate mathematical ideas, connect theory to programming, and explain technical concepts in a way that others can follow. It fits into my portfolio because it reflects both my academic interests and my broader approach to learning. Whether I am working on software, analytics, or math, I am most engaged when I can take a challenging idea, break it down, and turn it into something understandable and useful.
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