Humbert begins to retrace the trip he took with Lolita, scouring hotel registries for clues to the driver of the red car.
He visits all 342 hotels, and begins to gather clues about the abductor: clearly the man is messing with Humbert, as he leaves all sorts of suggestive names that indicate he is smug, clever, and knows French. Like Humbert, the man "was versed in logodaedaly and logomancy" (2.23.5), which means he has a big vocabulary. He also enjoys provoking Humbert with suggestive and allusive names.
Humbert realizes he had been on their tail a long time.