Error-correcting codes (ECC), found in coding theory, use methods to handle possible errors that may arise from electronic noise. ECC can be used in applications from performing magic tricks to detecting and repairing mutations in DNA sequencing. ECC, including Hamming Codes and Reed-Muller Codes, can be viewed through set theory, which give alternate perspectives on how these ECC work. In this research, Hamming Codes are explained through set theory and graph theory. This research also investigates further applications of the Hamming Code in a team competition and magic tricks. Reasonings as to how these applications are guaranteed to work given properties of the Hamming Code are also investigated. An investigation is done on the Hat Problem (a team competition) where all the conditions and outcomes of the game are explained through properties found in Hamming Codes. There is also an investigation on the Parity Card Trick, which is justified by elementary ECC concepts. Finally, a more advanced version of the trick is created.