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At Archduke Ferdinand’s gravesite, Lindsey gives her usual speech. She explains that the owner of the castle where the archduke was originally buried needed money and sold the corpse to the town of Gutshot. Four of Lindsey’s schoolmates approach, including her boyfriend Colin, tall and muscular, and a stunningly attractive girl named Katrina. This Other Colin reacts good-naturedly after Colin and Hassan prank the new arrivals by pretending to be French. Colin and Hassan start referring to The Other Colin as TOC. Back at the store, Lindsey, Colin and Hassan encounter Lindsey’s mother, Hollis. To Colin’s surprise, she recognizes him from a TV quiz show he appeared on a year earlier. Hollis invites the boys to join her and Lindsey for dinner at their home. Driving over in Hollis’s truck and Colin’s car, the four of them pass a factory. Colin learns from Lindsey that it makes something he did not even know existed: tampon strings.
Hollis and Lindsey’s enormous house is bright pink, like the store and Hollis’s truck. While Hollis and Lindsey prepare the meal, Colin works on his formula for predicting the length of a relationship and who will dump whom. (The equation correctly describes his relationship with Katherine I: after he agreed to be her boyfriend, she dumped him within three minutes.) Dinner is pleasant, after a little awkwardness over Hassan’s one-word prayer in Arabic. Hollis, who owns the tampon-string factory, offers the boys a summer job helping her with a project. Lindsey implies that they will stay at the house. The boys accept. Afterward, Colin and Lindsey chat. She used to be ugly and unpopular, she says, but deliberately adopted cool ways in high school. According to her, there is a method to being cool and popular. He tells her about his being a nerd, and his desire to matter.
When the topic of a job came up, Colin imagined a want ad for someone with his peculiar talents: skill at anagramming, fluency in eleven languages, and an encyclopedic memory. The job Hollis actually has for the boys involves taping interviews with people who work for her so she can put together an oral history of Gutshot. Lindsey will accompany the boys to get the interviewees to open up. The first interviewee is an old man named Starnes. The smell of Starnes’s house reminds Colin of the basement in the home of the most recent Katherine. She had taken him down there to watch The Royal Tenenbaums, a comedy about a family of prodigies. He wanted to kiss her, but he had a theory that the girl should make the first move. After the movie, when Katherine asked what Colin was good at besides languages, he answered that he was good with anagrams. For instance, her name could be turned into “their arcane trek.” She asked if he was good at anything else. At that point, he gathered his courage and said he was a good kisser. Katherine XIX and Katherine I are actually the same person: Katherine Carter.
Starnes tells the boys and Lindsey about himself and about Gutshot. The town got its name by being a center for “gutshot boxing,” in which all punches had to land between the belt and shoulders. Looking at Starnes’s old photos of him and his late wife, Colin thinks to himself that he will leave behind something more than just photos. The boys take Lindsey back to the store, for time alone with “the Lyford boy,” as Starnes called TOC. While Colin and Hassan wait outside, Hassan talks Colin out of calling Katherine. When they grow tired of waiting for Lindsey, Hassan fakes an asthma attack. Lindsey quickly leaves with them after Hassan explains that his inhaler is back at the house.
That evening, Colin overhears Hassan explaining to Lindsey and Hollis that Colin is able to remember so much partly because he finds everything interesting, but also partly through hard work. Colin thinks again that his only hope of accomplishing something original is his theory about relationships. He works some more on the formula while Hassan and Lindsey play pool. After Hassan has gone to bed, Lindsey debates with Colin. According to her, mattering is a misguided goal. “The bigger a deal you are, the worse your life is.” Also, she says, Colin needs to learn how to tell stories properly. A story should have a plot, and a moral, and romance. His Theorem about relationships will have romance, Colin retorts.
After Katherine I broke up with Colin, he continued to see her, since her father was his tutor. He was not at all obsessed with her, and yet for some reason he dated no one but Katherines from then on. They all dumped him. The cycle became boring after a while, but never less painful.
Chapter 7 revisits the missing piece motif when Lindsey, Colin, and Hassan finally visit the Archduke’s grave. There, Colin thinks about the Archduke’s two problems: first, that nobody cared about him, and second, that he had a piece shot out of his middle. Colin’s reflections on the Archduke lead him to explicitly resolve to both find his own missing piece and to achieve something that makes people notice him. In this moment, Colin essentially sets his goals for the metaphorical part of his coming-of-age journey.
Chapters 7 through 9 provide more insight into the setting of the novel and the characters’ relationship to it, including the fact that Hollis wants Lindsey to get out and experience something more despite how deeply she appears to care about the town. It seems likely that Hollis invites Colin and Hassan to stay because they represent outside forces with broader worldviews than Lindsey has access to in Gutshot. The job that Hollis hires the boys to do—interviewing former and current workers for an oral history of Gutshot—serves as a device by which the boys learn about Gutshot and the important role the factory plays in the community. As Colin and Hassan record interviews, they start to see how many people in Gutshot rely on the factory for their livelihood and survival.
These chapters continue the examination of friendship as they show the friendship evolving between Lindsey and Colin, who have a lot in common. Like Colin, Lindsey is very smart, and despite growing up in a tiny town, she speaks more than one language and feels like an outsider among her peers (although unlike Colin, she has found ways to fit in). More importantly, Lindsey challenges Colin in a way that nobody but Hassan seems to do. Lindsey lets Colin know that she is not impressed by him showing off his knowledge, and she also tells him that his storytelling needs improvement. Together, these details develop the theme of friendship by suggesting that one of the ways true friends support one another is by challenging each other to be better.
Colin’s work on his formula provides a narrative device by which Colin reveals information about his romantic past, underscoring the thread of romantic love. As he finetunes his formula, flashbacks reveal details from relationships with various Katherines that Colin uses to test the formula and confirm whether the predictions it makes reflect reality. As these flashbacks further the plot by allowing Colin to improve his formula, they also provide insight into his past relationships, some of which hardly seem like real “relationships” at all. Many of these details suggest that Colin has been more invested in the narrative he has created about “relationships with Katherines” than in the actual relationships with the girls themselves. In particular, the fact that the most important variable for Colin seems to be who broke up with whom implies that his concept of romantic love is stunted and grossly oversimplified.