Humbert Humbert spends nearly four months trying to track down the man Lolita ran off with. He visits 342 hotels, motels, etc., and at each of them, he checks the guest register for evidence. The man seems to have anticipated Humbert’s investigation, and has left a trail of mocking pseudonyms: Arthur Rainbow, Donald Quix, Harold Haze, G. Trapp.
The number of hotels and motels Humbert visits is the same as the Haze’s address in Ramsdale, suggesting a pattern in Humbert’s fate—or at least in his own imagination. As always, it is difficult to tell the two apart. The pseudonyms left by the man Humbert is pursuing (Quilty, though Humbert doesn’t know it yet) are all jokes: some of them about literature, and others about Humbert. Arthur Rainbow is a mangled version of Arthur Rimbaud, a French poet whose work Humbert includes in the textbook he is compiling. Donald Quix is a play on Don Quixote, a famously naïve and idealistic knight from a novel of the same name. Harold Haze is Lolita’s deceased father, and G. Trapp is Humbert’s uncle, with whom Quilty shares a strong resemblance.
By interpreting these pseudonyms, Humbert comes to realize several things: that the affair between Lolita and this person probably began in Beardsley; that Lolita gave this man the plan of her current road trip with Humbert in advance; that Lolita has told the man intimate details about her and Humbert's life; and that this man is very similar in personality and education to Humbert himself. Nevertheless, the search ends in failure. Humbert returns to Beardsley.
The pseudonyms Humbert finds enable him to recognize that Lolita was not been “kidnapped,” but cooperated in her own escape. How else would the man she fled with know the details about Humbert’s personal life contained in his mocking pseudonyms? Quilty’s literary sophistication and mocking arrogance mirrors Humbert’s own. The idea that some people have “doubles,” is an important motif throughout this novel, as well as within Nabokov’s other books. The theme of the double was popular in nineteenth century Russian literature, a tradition by which Nabokov was strongly influenced.