I believe I do have a timeline of events that you might find illuminating.
On a train journey to Lyon, Vanessa points out another traveller. She presents a number of theories about him based on what she has observed in his appearance and behaviour.
They exchange some ideas about the man, until Walter proposes a wager – whoever can tell the other most about the man after three minutes will win a piece of crystalised ginger.
After Vanessa accepts, Walter simply walks over to the man and introduces himself. He invites the man back to their table and relays what he has learned about him to Vanessa. He then eats the ginger.