Kusanagi and Yukawa discuss many of the more tricky and mystifying aspects of the murder case, with Yukawa encouraging Kusanagi to share different theories and consider various possibilities about what could have happened. All of the problems that confound the police have, in fact, been purposely contrived in order to mislead and deceive the police about the true nature of the murder. In this sense, they attest to Ishigami's genius in designing a cover-up that is able to prevent the police from cracking the case. Yet not all people are as perplexed and at a loss as the detective are in the matter, Yukawa being the notable exception.

True to his calling as a physicist, Yukawa in this chapter demonstrates his preference for experimentation and observation. He visits Ishigami and asks probing questions in order to gather evidence that will either support or refute the hypotheses that he discusses with Kusanagi in the beginnig. It's for this reason that he asks whether Ishigami has an interest in driving. In order to deflect suspicion from Ishigami about his motives for visiting, Yukawa also devises a clever excuse, namely that the police wish to enlist Ishigami as a spy to observe Yasuko. Just as Ishigami is skillful in covering up aspects of the murder case and his involvement in it, so is Yukawa skillful in in covering up the purpose of visit.

Much of the communication between Yukawa and Ishigami occurs on multiple levels, including figurative and literal. Yukawa's parting challenge to Ishigami about another math problem (i.e. the question of whether it's easier to devise an unsolvable problem or to solve that problem) is an example of this, since it indirectly conveys to Ishigami Yukawa's nascent, if not totally well-developed, suspicions about what happened.

Ishigami's interaction with the students and Morioka in particular is both amusing and revealing in what it shows of Ishigami's character, specifically how mathematics dominates Ishigami's worldview. We see that Ishigami is unable to design simple test questions that will make it easier for the students to pass the class. He does his job strictly by the book, maintaining an absolute standard, even if it means failing most of the students. From the perspective of ordinary people, his unrelenting insistence that the students keep taking make-up tests until they meet a minimum standard is excessive and over-kill. The staff and administration understand implicitly that the make-up tests are a mere formality, but Ishigami understands his duties in a very literal and inflexible way, not allowing such emotions as pity and empathy to get in the way. Also indicative of his insensitivity is his unwillingness to loosen his standards for students who won't need mathematics for their future career studies. This rigid insistence on the students' need for mathematics reflects the all-pervasive nature of mathematics in his own life. When challenged by students such as Morioka to justify the teaching of integral and differential calculus for students such as Morioka, Ishigami goes into a lengthy explanation about how calculus is relevant to motorbike racing. This demonstrates how everything, including covering up a murder case, are matters of mathematical thinking for Ishigami.

Despite his response to Morioka, Ishigami is clearly not just a person for whom mathematics is the be-all and end-all of his existence, as his reaction to Kudo demonstrates. When Ishigami notices Kudo getting along well with Yukawa, his involuntary reaction is one of frustrated jealousy, which will tip off Yukawa, ever the keen observer, of his true feelings for Yusako and, by implication, the true nature of his role in the murder. This obvious insecurity on Ishigami's part will perhaps incline the reader to view Ishigami unfavorably, together with the unrelenting and harsh manner in which he treats his students. His instructions to Yasuko may come off as being just as overbearing as his attitude towards the students. So while the reader may sympathize with him on one level, given the degree to which he's made sacrifices for Yasuko's well-being, they may also start to feel uncomfortable with his being so prone to jealousy, especially given the way he adheres to rules and mathematical regularity at the expense of human compassion when it comes to his students.