On optimal solutions of a family of two jugs problem

On optimal solution of the general two jugs problem

Let M(m, n) be the integer sequence of all non-zero measurable amounts less than m + n that are obtainable by two unmarked jugs of capacities m and n units. We introduce the concept of dual sequences which describe the correspondence relation between M(m1, n1) and M(m2, n2), where 0 < m1 < n1, 0 < m2 < n2, m1 + n1 = m2 + n2 and gcd(m1, n1) = gcd(m2, n2) = 1. Some illustrative examples are provided. AMS subject classification: 11A07, 68W1, 97F60.

On optimal solutions of a family of two jugs problem

Citations

On optimal solution of the general two jugs problem

On duality of sequences of measurable amounts of the jug problem

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