58 pages • 1-hour read
A modern alternative to SparkNotes and CliffsNotes, SuperSummary offers high-quality Study Guides with detailed chapter summaries and analysis of major themes, characters, and more.
Content Warning: This section of the guide includes discussion of domestic abuse, gender discrimination, suicidal ideation and self-harm, attempted death by suicide, graphic violence, and death.
“Ishigami had first seen the Engineer about ten days ago. He wasn’t used to life along the river yet, still drawing an imaginary line between himself and the blue vinyl sheets. Yet here he stayed, not knowing how to live on his own without a home.”
Ishigami’s routine walk from his apartment to his school, described in the first chapter, is full of important clues about the mystery plot to follow. The most crucial detail is the tent city of unhoused people, where he notes several figures that he has offhandedly and irreverently nicknamed. Ishigami’s focus on “the Engineer” in this scene contrasts with the man’s missing presence in later descriptions of the tent city, hinting at the novel’s conclusion.
“This man was a curse on her and her daughter. She had to get him off her daughter. She had to be rid of him. If she let go now she might never get another chance.”
This passage illustrates Yasuko’s fear and desperation as she struggles against the violent Togashi, making it clear that her motives for killing him are primarily self-defense and the need to protect her daughter. Earlier in this scene, her reflection that the police never helped her against Togashi in the past indicates that the traditional social structures in Japan have left her with no other options to ensure her survival.
“Murder is murder. Everything else is just details.”
Having killed Togashi, Yasuko considered turning herself in, but Misato objects, saying that Togashi’s death is not her fault and she should not be punished for it. This bleak statement is Yasuko’s response, and the line succinctly summarizes one view of justice and morality depicted in the novel and contributes to the theme of Navigating Imperfect Justice and Moral Ambiguity. In this view, right and wrong are rigidly defined terms, and in this worldview, murder is always wrong, no matter the circumstances.
“Whatever you do, don’t panic, he told himself. Panicking wouldn’t help them reach a solution. And he was sure their problem had a solution. Every problem had one.
Ishigami closed his eyes. It was a habit he had developed when confronting particularly ornery mathematical challenges—all he had to do was shut out all information from the outside world, and the formulas would begin to take shape.”
This passage introduces the symbol of mathematics, which is the lens through which Ishigami views and responds to the world. Ishigami uses math to analyze and control every situation in his life, and this mindset allows him to divorce himself from the emotional repercussions of covering up a murder. His reliance on such logic suggests that he possesses a certain moral flexibility, and this fact complicates the novel’s focus on Navigating Imperfect Justice and Moral Ambiguity.
“What they thought to be the victim’s clothes had turned up, stuffed into a five-gallon oil can, several hundred yards from the place where the body was found. The clothes were partially burned. There was a jacket, a sweater, pants, socks, and underwear. Forensics guessed that the killer had set fire to the clothes and then left. But the fire had gone out before finishing the job, and they hadn’t burned as well as he had hoped.”
This scene in Chapter 3 is vital to the puzzle-like mystery plot. Each clue is meticulously described for the readers’ benefit, in keeping with the genre expectations of honkaku stories, which always provide enough clues to allow readers to solve the mystery themselves. The details included here are important to the false trail that Ishigami leaves for the police, which Yukawa later deconstructs with practical experiments like burning clothes to see what happens.
“Yukawa sighed. ‘I don’t use the word genius lightly, but it fits him well. One of our professors said he was the kind of student you only see once every fifty or a hundred years. […] When you saw him, it was usually from the back while he sat hunched over a desk—that’s how he got the nickname ‘the Buddha.’ A term of respect, of course.’
Kusanagi nodded. It was odd to hear Yukawa talk about someone even more brilliant than himself. The detective had always thought of his friend as the genius, but he supposed that even when you were at the top, there was always something higher.”
Yukawa’s past friendship with Ishigami is a significant element of the plot for several reasons. First, he is the only one who understands the true nature of Ishigami’s genius. Second, without this personal connection, Yukawa would not have become involved in the case, and Ishigami would likely have succeeded in covering up the murders. Finally, Yukawa’s feelings of friendship create emotional tension and contributes to the novel’s examination of The Morality of Love and Self-Sacrifice. Kusanagi’s thoughts also indicate the level of Yukawa’s own brilliance, marking Yukawa and Ishigami as intellectual equals.
“This might’ve been the first time he had talked this much to another person since graduating. Who else could understand him but Yukawa? Who would even recognize him as an equal?”
In this scene, Ishigami reflects on his friendship with Yukawa, echoing Yukawa’s comments in the previous chapter. Just as Yukawa views Ishigami as a genius who is equal or superior to himself, Ishigami views Yukawa in the same way. He believes that Yukawa is his only equal, and this fact later worries him and proves to be his downfall.
“Suddenly she wondered what would happen if she got close to another man. Would Ishigami keep helping her like he had? Would he keep solving all their problems? Yasuko decided that it might be best not to have dinner with Kudo. And if they did meet, not to let Ishigami know about it. But as soon as the thought came, a strange feeling of anxiety seized her. How long would this last? How long would she have to avoid Ishigami’s watchful eyes?”
Yasuko’s concern over how Ishigami might react to her decision to date Kudo is an important element of The Morality of Love and Self-Sacrifice. She wonders what she owes to Ishigami for his protection, and she fears that he will impose control over her for the rest of her life. This concern highlights the potential burden that love places on the recipient, no matter how well-intentioned the giver may be.
“Which is harder: devising an unsolvable problem, or solving that problem? And it’s not an empty question. Unlike the Clay Mathematics Institute prize people, I guarantee this puzzle has an answer.”
The mathematical theorem that Yukawa poses to Ishigami is another example of the author’s use of mathematics as a symbol. More importantly, this math problem encapsulates the central conflict of the novel, including both the murder itself and the competition that arises between Yukawa and Ishigami, in which Ishigami tries to devise an unsolvable problem and Yukawa attempts to solve it.
“He had expected the police to identify the murder weapon. Which was why he had exchanged the Hanaokas’ kotatsu with his own. Their old kotatsu—the real murder weapon—was packed away in his closet. As luck would have it, the cord on his old kotatsu was different from the one on theirs. If the detectives came back and examined that cord, they would immediately realize it was a dead end.”
This passage is one of many examples of Ishigami’s habit of successfully anticipating the police’s actions and manipulating the investigation. Using his brilliance and logic, he accurately calculates each move that the police will make and accounts for those variables in his plan, as illustrated by his attention to the kotatsu cord. The author reveals each of these details slowly, controlling how much of the complex puzzle the readers can see at any given time.
“They were right, of course. He did go to the shop every day just to see her. And he realized that unconsciously he had expected her to notice how he felt. Still, it made his entire body hot with shame to think that someone else, a third party, had noticed first. How they must have laughed to see an ugly man like him head over heels for a beautiful woman like her.”
In previous scenes, Ishigami has remained unaware that others, such as Yasuko’s employers, noticed his attraction to Yasuko. He believed that he had hidden his feelings well, but he now becomes aware of his mistake for the first time. This fact reveals the inherent irony that although Ishigami’s intellectual genius is fully acknowledged, he nonetheless lacks the emotional intelligence to conceal his own feelings. This quirk is crucial to the plot, for Yukawa also notices Ishigami’s fixation without Ishigami being aware that he has given himself away.
“Yukawa had shaken his head, his eyes cool. ‘It’s not a question of temperament. Murder isn’t the most logical way to escape a difficult situation. It only leads to a different difficult situation. Ishigami would never engage in something so clearly counterproductive. Of course,’ he had added, ‘the converse is also true. That is, he’s quite capable of committing an atrocity, provided it’s the most logical course of action.’”
In this scene, Yukawa’s comments highlight the symbolic importance of math while also revealing the fact that such a logical worldview may warp Ishigami’s sense of morality. Yukawa’s belief that Ishigami could commit murder and even defend it as the logical choice proves accurate and contributes to the theme of Navigating Imperfect Justice and Moral Ambiguity. In short, Ishigami’s logic-based moral code contrasts with the accepted ethical rules of society and the legal system.
“Still, Kusanagi trusted Yukawa’s skills of observation and deduction, almost to the point that, if Yukawa thought something was so, the detective assumed it was correct unless proven otherwise.”
Kusanagi’s trust in Yukawa reflects Yukawa’s brilliance and analytical skill and serves as a testament to their friendship. Even so, Kusanagi’s uncritical trust in Yukawa’s observations lead him to investigate Ishigami merely because Yukawa has demonstrated an interest in the man; at this point, Kusanagi still has no concrete evidence to suggest that Ishigami is connected to the case.
“It suddenly occurred to her that this man knew about Ishigami’s interest in her and wanted to know why it had started.
Yasuko realized for the first time that she had never given a moment’s thought to that herself. She knew from years of experience that she wasn’t the kind of beauty with whom men fell head over heels in love at first sight. It had to have been something else.”
One question in the novel is why Ishigami is so loyal and devoted to Yasuko. Yukawa wishes to understand this, and the implication is that Ishigami’s motives may justify his actions. Meanwhile, Yasuko suddenly acknowledges her own false assumption, for she previously placed Ishigami in the same category of other men with crushes, and she now realizes that she does not understand the depth of his feelings at all.
“‘They’re not tough, though. I merely take advantage of the blind spots created when students assume too much. And they usually assume too much.’
‘Blind spots?’
‘For instance, I give them a question that looks like a geometry problem, but is in fact an algebra problem.’”
In this dialogue between Ishigami and Kusanagi, Ishigami explains the way he writes test questions for his students. This conversation becomes an extended metaphor for disguising a problem to look like a different kind of problem entirely. This conversation proves instrumental to Yukawa’s ability to dissect Ishigami’s puzzle and solve the mystery.
“Yukawa nodded, satisfied. ‘Too bad it’s impossible for you and me ever to be off the clock. Like it or not, we’re stuck in the cogs of society. Take them away, and our clocks spin out of control. Or rather, we are the cogs in the clockworks. […] The world needs its cogs, all of them; even a cog may say how it gets used. In fact, only a cog may determine its eventual meaning in the system. That’s what I wanted to tell you,’ Yukawa said, staring Ishigami in the face.”
In this conversation between Yukawa and Ishigami, Yukawa introduces the symbolism of cogs, which he uses in an extended metaphor to explain The Inherent Worth of Individuals. This belief that all cogs have a place in the system—or that all people have value in the world—underpins Yukawa’s approach to Navigating Imperfect Justice and Moral Ambiguity and leads him to the conclusion that Ishigami must be punished for his crime.
“The mathematician turned his back on Yukawa and strode into the school, tote bag clutched tightly in his arms. It’s over, he thought. The physicist had seen through everything.”
Following their conversation about cogs, Yukawa carefully dissects every piece of Ishigami’s puzzle, demonstrating that he knows the truth without explicitly accusing Ishigami of being the murderer. Ishigami knows that the first layer of his plan has been ruined, leading him to the decision to turn himself in under the guise of a stalker. This development adds yet another twist to the plot.
“There weren’t any gaping holes in the story. Everything he’d said about the body’s condition and the scene of the crime matched what the police knew. Since none of the details had been released publicly, it was easier to think that he was telling the truth than to believe the alternative.”
Kusanagi is suspicious of Ishigami’s confession, but as Ishigami planned, his answers neatly account for every detail in the case. Ishigami believes that the police will take the easy route and accept this story without investigating further. Without interference from Yukawa in the next chapter, this would likely be true, as Kusanagi reflects in this passage.
“Kusanagi looked back up. He breathed in sharply. The physicist’s face was twisted with grief; he pressed one hand to his forehead and squeezed his eyes closed.
‘Of course I don’t want him to be accused of murder. I just don’t see any way out of it.’”
Although the narrative never depicts Yukawa’s perspective, his feelings are made clear through Kusanagi’s observations of his facial expressions. Yukawa is pained by the knowledge that his friend Ishigami is guilty of murder. He has tried to find a way to understand and potentially clear Ishigami of the crime, but he now acknowledges that he cannot. These nuances contribute to the novel’s examination of the interplay between love and justice, for he determines that his friendship is not enough to convince him to abandon his own moral code.
“‘There’s something I need to tell you, but you my friend, not you the detective. And I can’t have you telling anyone else, ever. Not your police chief, not your friends, not even your family. Can you promise me this?’
Kusanagi saw a terrible urgency in the eyes behind the wireframe glasses. He could tell that Yukawa felt forced into making a decision he wasn’t ready to make.
He wanted to say, ‘It depends on what you tell me.’ But Kusanagi swallowed his words. If he said that, Yukawa would never look at him as a friend again.”
In comparison to the intellectual conflict between Yukawa and Ishigami, the tension between Kusanagi and Yukawa is relatively minor. However, this dynamic is still important to their character development, and to the plot. Their respective roles as detective and consultant sometimes conflict with their deeper roles as friends, and in this moment, Yukawa asks Kusanagi to choose one or the other. Kusanagi understands that his decision will alter not only the outcome of the case but also their future as friends.
“He has made a terrible sacrifice in order to protect you, you know. A sacrifice so great, ordinary people such as you and I couldn’t even imagine doing such a thing. I’m sure that, from the night it all happened, he was prepared to take your place in a jail cell, should the situation call for that. His entire plan was constructed around that commitment. […] Who could possibly follow through on such a plan? Ishigami knew it would be near impossible himself. That’s why he cut off his own path of retreat—so he would never be able to turn back once things were put into motion.”
Speaking to Yasuko, Yukawa lays out the facts of the case, including all the twists of Ishigami’s complex plan. In this passage, he focuses on the sacrifice that Ishigami has made, highlighting The Morality of Love and Self-Sacrifice. Crucially, Ishigami has not merely sacrificed his own safety and freedom by taking the blame for Yasuko; he has also sacrificed his own morality and innocence, which in Yukawa’s mind, is far worse.
“Yukawa took a deep breath. ‘Ishigami was the killer. Not you, or your daughter. He’s not turning himself in for a crime he didn’t commit. He’s guilty of murder.’
Yasuko gaped, not comprehending what she was hearing.
‘However,’ Yukawa added, ‘that body did not belong to Shinji Togashi. That was not your ex-husband. He was a complete stranger made to appear to be your ex-husband.’
[…]
‘Looks like you finally understand what I’m trying to tell you,” Yukawa said softly. ‘Yes. In order to protect you, Ishigami committed murder—on March 10. The day after Shinji Togashi was killed.’”
This passage reveals the final twist of the narrative. The novel has strategically concealed and revealed various details to create the impression that Ishigami has merely covered up a murder rather than actively committing a second one. Now, Yukawa explains how all the clues add up, including the presence and disappearance of the Engineer, and thus revealing the full extent of Ishgaimi’s complex plan.
“She had never encountered such deep devotion. She hadn’t even thought it existed. Yet Ishigami had it, hidden away beneath that expressionless mask of a face—the kind of passion unfathomable to the average person.”
Yasuko is stunned by the depth of Ishigami’s feelings, having never suspected them to be present in his mind and motivations. More importantly, she feels burdened by his devotion, and this dynamic once again calls into question The Morality of Love and Self-Sacrifice. Her thoughts suggest that in certain extreme circumstances, love and protection can become harmful to the recipient.
“Ishigami’s life changed after he met the Hanaokas; in that moment he was renewed. All thought of suicide faded. Joy returned to his daily rituals. […] He had added the coordinates of Yasuko and Misato to the matrix of his life, and to him, it seemed like a miracle had occurred.”
In a flashback, Ishigami at last reveals why he has remained so loyal and devoted to Yasuko. In an ironic twist, he believes that he owes Yasuko and Misato his life, just as Yasuko fears that she owes him hers. This development uncovers yet another layer to the presumed obligations of love.
“Ishigami stepped backward, shaking his head convulsively. His features were twisted with pain.
Then he whirled around, pressing his fists to his temples, and howled—a long, roaring howl like that of a beast. A cry of confusion and desperation. A cry that tore at the hearts of all who heard it.”
The final scene focuses not on Misato’s confession or Yukawa’s service to the interests of justice, but on Ishigami’s despair. This narrative choice implies that all the pain that the characters have suffered is now meaningless. This moment indicates that there is no winner in this case: no moral good or righteousness to be had in the conclusion.



Unlock every key quote and its meaning
Get 25 quotes with page numbers and clear analysis to help you reference, write, and discuss with confidence.