On duality of sequences of measurable amounts of the jug 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. Copyright © 2017 Research India Publications.