In this chapter, we are introduced to Yukawa Manabu, a physics professor at Imperial University, whom we discover to be extremely intelligent. His challenge to Kusanagi to "look at the situation logically," echoes Ishigami's last words from the previous chapter: "Logical thinking will get us through this." This scene establishes Yukawa and Ishigami as doppel-gangers or mirror-images of each other. While Kusanagi and Yasuko are faced with a difficult problem for which they can't find a solution, both Yukawa and Ishigami urge their counterparts to think logically.

Yusako is frustrated by the fact that the laws are not in her favor: she is a murderer, despite the fact that she was being harassed by her ex-husband and that her daughter was in danger of being beaten to death by the very same ex-husband. Similarly, Kusanagi is frustrated by the fact that the rules of chess don't allow him to use pieces captured from his opponent. They both are forced to deal with a situation whose rules do not accommodate their desires.

Between Kusanagi and Yukawa, the latter is clearly the brain in the relationship. For most of the forty minutes that they are playing chess, it is Kusanagi who spends most of the time pondering his next move. When Kusanagi complains that "chess is boring," Yukawa pokes fun at him with a little friendly sarcasm, saying: "With you, yes." Their relationship is one characterized by competition and verbal jousting, but they are friends nonetheless. Their discussion of the case will likewise be characterized by a similar battle of wits, with Yukawa providing valuable insights based on his capacity for non-conventional thinking.

We are also introduced to the junior detective, Kishitani, who works under Kusanagi. Kishitani is somewhat naive about murder cases. As a result, he is somewhat perplexed by Kusanagi's remark that "this is going to be a real tricky one. Heaven or hell," which serves to emphasize Kusanagi's experience. Because of this experience, Kusanagi is a good judge of character and is thus able to accurately assess the character of Ms. Yamabe, owner of the stolen bike, whom he correctly predicts will ask to be reimbursed for the flat tires.

Besides Kishitani, there is also Mamiya, the division chief who is Kusanagi's superior officer. He is a typical "hard-headed" police chief, gruff in his manner, who demands results and has no patience for whining. Thus, Kusanagi finds himself caught between inexperience and naivete, on the one hand, with all its associated inability to accurately gauge the reality of human nature, and the pressures of the police bureaucracy, represented by Mamiya, with all its associated deficiencies, namely a lack of creative thinking that goes outside the box. This is the dynamic that will underlie the interactions among the police throughout the novel.

This chapter also makes several assumptions about the case that the reader will take for granted throughout the novel. For example, March 10 is the date established for the day of the of murder, even though this is based on an autopsy of the dead body as well as the time that the bike was stolen. In addition, neither the fingerprints on the bike nor the hair found in the hostel are positively matched to Shinji Toagshi. The fingerprints and the hair are only matched to the corpse found at the crime scene, but not to Shinji Togashi. These assumptions will guide the detectives and the reader throughout the rest of the novel.