Autors: Velchev, A. P., Petrov, Ph.P. Title: A Trial for Systematization of Methods for Generating and Solving Variations of Discrete Optimization Problems and the Three Jugs Problem as an Example Keywords: Discrete Optimization, Three Jugs Problem, Didactics Abstract: Generalized form of the problem is: “3 vessels of volumes M, N and P contain respectively m, n and M(m+n) liters liquid, where M=N+P, N >P. Divide the liquid in two equal parts.” The solution is frequently done by trialerror. Perelman provided a “billiard” solution to the problem without prescriptions how to guess to solve it like this. There are numerous articles on this topic, but there are no known to us attempts for exhaustive analysis, synthesis and systematization of them. We consider briefly the most interesting ones with didactics perspective. We prescribe ideas for solutions, generalizations, investigations, generating of new problems and proofs, based on promising visualization of the quantities of liquid in the three vessels by projective coordinates of points in a Euclidean plane. The pourings are visualized by directed segments between the respective points. This visualization is good for finding all possible solutions, the optimal one in concrete steps, etc. References Issue

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