The Name Tag Problem is a thought experiment that, when formalized, serves as an introduction to the concept of an orthomorphism of $\Zn$. Orthomorphisms are a type of group permutation and their graphs are used to construct mutually orthogonal Latin squares, affine planes and other objects. This paper walks through the formalization of the Name Tag Problem and its linear solutions, which center around modular arithmetic. The characterization of which linear mappings give rise to these solutions developed in this paper can be used to calculate the exact number of linear orthomorphisms for any additive group Z/nZ, which is demonstrated in the third section. The final section establishes the equivalence between solutions to the Name Tag Problem and orthomorphisms of Z/nZ.
"The Name Tag Problem,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 21
, Article 9.
Available at: https://scholar.rose-hulman.edu/rhumj/vol21/iss1/9