  In this paper we consider two variants of the Secretary problem: The
Best-or-Worst and the Postdoc problems. We extend previous work by considering
that the number of objects is not known and follows either a discrete Uniform
distribution $\mathcal{U}[1,n]$ or a Poisson distribution
$\mathcal{P}(\lambda)$. We show that in any case the optimal strategy is a
threshold strategy, we provide the optimal cutoff values and the asymptotic
probabilities of success. We also put our results in relation with closely
related work.
