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We consider discrete bit loading problems for multicarrier systems employing DMT (discrete multitone). In this context two problems are of practical interest, namely margin maximization (also known as margin-adaptive loading) and rate maximization (also known as rate-adaptive loading). In the current literature the two problems are regarded as different and different algorithms are usually provided in order to solve them. In this work we will be able to establish a duality between the two problems. That is, a tight connection between them such that, under certain hypotheses, the same solution solves both problems. This result is interesting both from the theoretical and the practical point of view. With regard to the former it provides a unifying framework for the analysis of two apparently different problems. With respect to the latter it allows an easy derivation of loading algorithms for one of the problems whenever the corresponding algorithms for the other are known. Examples of application of the duality are also provided.