Robbery-homicide prompts Beckett to invite Demming to assist on a case, giving Castle a ringside seat to their budding romance. When it becomes clear that the two men have very different ideas about how to proceed, the investigation becomes an unspoken competition for Beckett's attention, one in which each man races to solve the case, as Beckett referees between her two admirers.
Spoilers ahead. Coverage follows the scope labeled below.
Complete story — includes the ending
Beckett asks Demming to help her and Castle investigate the murder of a men's cosmetics mogul and the theft of his rare book collection, prompting the two men to fall into competition with each other to impress Beckett by proving their own theory in the death correct. As the case develops, it becomes obvious to Castle that, despite his efforts at solving the case, Beckett's relationship with Demming has gotten serious.