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This paper presents an extended project that offers, through American football, an application of concepts from enumerative combinatorics and an introduction to proofs course. The questions in this paper and subsequent details concerning equivalence relations and counting techniques can be used to reinforce these new topics to students in such a transition-to-proofs-type course or to offer an application of known theoretical mathematics to students with more advanced understanding in the major.

This paper describes the n-queens problem on an n x n chessboard. We discuss the possible symmetries of n-queens solutions and show how solutions to this classical chess question can be used to create examples of colorful artwork. [ABSTRACT FROM AUTHOR]