  This paper establishes a close relationship among the four information
theoretic problems, namely Campbell source coding, Arikan guessing, Huleihel et
al. memoryless guessing and Bunte and Lapidoth tasks partitioning problems. We
first show that the aforementioned problems are mathematically related via a
general moment minimization problem whose optimum solution is given in terms of
Renyi entropy. We then propose a general framework for the mismatched version
of these problems and establish all the asymptotic results using this
framework. Further, we study an ordered tasks partitioning problem that turns
out to be a generalisation of Arikan's guessing problem. Finally, with the help
of this general framework, we establish an equivalence among all these
problems, in the sense that, knowing an asymptotically optimal solution in one
problem helps us find the same in all other problems.
