On-line selection of an acceptable pair

A sequence of objects with independent, identically distributed qualities is presented to a selector who must choose two on-line, i.e. without anticipation or recall. The selector's aim is to obtain a satisfactory pair as quickly as possible. Two versions of the problem are considered, and optimal selection rules are derived and compared. An investigation is also made of a heuristic rule suitable for a selector who has no prior knowledge of the nature of the object sequence.