[bluesbassman]

I peeked at the solution to this stopping problem on wiki.

I assume that for both Mr. Sklanky's formulation and the "secretary" variant described on wiki, there is no known maximum theoretical upper bound on the value (in this case attractiveness) of a given candidate. That is, no matter how pretty a given woman is, the next one could be prettier. In other words, the domain of possible values upon which the candidates are judged is an open set. (Is this assumption correct?)

Suppose, however, we can define a finite upper bound? In Sklanky's example, suppose it is known the attractiveness of each woman can be assigned a value on the closed interval [1, 10]. (Non-integer values are allowed.) Thus, if a perfect 10 walks through the door, we can immediately stop.

Does this change the stopping problem solution? If so, how?

Edit: Actually, a bounded domain is not sufficient; it must also be closed. For example, if the attractiveness of the women can be assigned values on the open set (1, 10), then (I think) the published solution applies. (In that case a perfect 10 is excluded.) So modify my preceding question to consider domains which are both bounded and closed.