Thompson: “I don’t think any word can explain a man’s life. No, I guess Rosebud is just a piece in a jigsaw puzzle—a missing piece.”
Thompson says this at the very end of the film as he’s leaving Xanadu to catch his train. He’s been unsuccessful in his quest to find out who, or what, Rosebud is. As he walks through the rooms of Xanadu, crowded with the late Kane’s possessions, he picks up a jigsaw puzzle, which prompts the metaphor. Citizen Kane is about the jigsaw puzzle that is a person’s life, and what Thompson has been doing since the beginning of the movie is trying to put that puzzle together. Thompson even has a snapshot of sorts to work from, in the form of the newsreel seen very early in the film. In spite of the information he already has, Thompson ultimately fails in his efforts to put Kane’s life together simply because he’s missing one key piece: Kane himself, who is dead.
This quote relates to more than just Kane’s life. The state of Kane’s later relationship with Susan becomes clear when we see her putting together endless jigsaw puzzles as she sits, day after day, bored and isolated, in Xanadu’s vast rooms. Although Welles always maintained that Kane was not modeled on Hearst, and, more vehemently, that Susan was not modeled on Hearst’s mistress, Marion Davies, the fact is that Herman Mankiewicz, a writer of the script for Citizen Kane, did spend quite a bit of time at San Simeon with Marion Davies and would have known of her passion for jigsaw puzzles. The references to jigsaw puzzles supply yet more evidence for the connection between Hearst's real life and Kane's fictitious life.