Is it possible to give a strategy for the combined problem of http://en.wikipedia.org/wiki/German_tank_problem and http://en.wikipedia.org/wiki/Secretary_problem So I'm observing tanks with serial numbers and I'm allowed only the keep the last one. I also don't know how many there are in total. My task is to (increase change of getting the highest number) or (achieve the highest average serial number on the tank I'm keeping). The distribution of serial numbers is uniform. Another case would be if it's normal. Basically it is the secretary problem with an unknown number of applicants, but moreover this unknown number if applicants has to be estimated given the observed incoming samples. The assumed distribution of all samples could be uniform or maybe also normal. Has anyone heard of an article where this problem is considered? Or how do I find such an article?