Discrete Mathematics instructors and students have long been struggling with various labelling and scanning algorithms for solving many important problems. This paper shows how to solve a wide variety of Discrete Mathematics and OR problems using assignment matrices and linear programming, specifically using Excel Solvers although the same methodology can be expanded to other linear programming software. The paper extends the assignment matrix methodology in linear programming to a wide range of Discrete Mathematics and OR problems, including knapsack problems, independent sets, matching problems, max flow problems, travelling salesman problems, and transportation time and cost problems. By relaxing the constraint that assignment matrices must be binary, this linear programming approach can be extended to a wide range of increasingly complex problems. The paper goes on to show how to apply these different assignment matrices to a variety of specific problems documented in the literature using Excel[R] Solver and Premium Solver. (Contains 3 tables and 18 figures.)