Kiddushin Conundrum

At a typical wedding, there can be no doubt who the kallah is. But hundreds of years ago, a chassan got himself into a jam due to a lack of specificity. Tosfos (Kiddushin 52a) recount a fascinating story that occurred with Rav Oshaya HaLevi’s son. Details are somewhat sketchy, but the following may be what occurred.
There was a wealthy individual with several daughters. Someone suggested that Rav Oshaya’s son might be a good match for one of the daughters. Rav Oshaya’s son checked out the family and thought that one of the wealthy man’s daughters would make a good shidduch. It seems that the father specifically agreed to allow the prospective chassan to marry his oldest daughter. However, it is unclear if there ever was a formal agreement. The wealthy man was authorized to act as an agent on behalf of his daughters to accept kiddushin. In other words, his future sons-in-law were expected to give the wedding bands to him instead of to their kallos directly. Rav Oshaya’s son followed this procedure, handing the wealthy man a ring and declaring: “Your daughter is betrothed to me.” He failed to specify the daughter he intended to marry. Which daughter is he married to?