Episode 1 of "A Killer Paradox" unfolds amidst the cozy confines of Lee Tang's parents' abode. Tang, an unassuming college student recently discharged from military service about six months prior, finds himself amidst the bustling preparations for his sister Yeong's impending nuptials. His family expresses concern over his apparent lack of direction since his return, while Tang reveals his intentions to embark on a working holiday in Canada.
Back at his college, Tang engages in animated conversations with his chums, Gyeong-hwan and Mi-yeong, expressing his dissatisfaction with the mundane routine that has persisted since high school. He harbors a deep desire for something extraordinary, a yearning that fuels his dreams. His apartment, however, stands as a stark contrast to his aspirations, a chaotic refuge reflecting his neglected life. As he unboxes a package, a beautifully framed photograph of the majestic Rocky Mountains comes into view, igniting his wanderlust. Tang attempts to hang it on his wall but struggles with the mundane task of driving a nail into the surface.
Transitioning to his job at a convenience store, Tang encounters a drunk customer who demands cigarettes and mistakes the establishment for a restaurant, ordering food with a flair that borders on comical. His companion, a kinder soul, intervention buys the food and the pair eventually depart, leaving behind a trace of laughter and chaos. At closing time, Tang's boss enters, urging him to head home. Tang halfheartedly asks for a hammer to hang his photograph, but his boss, engrossed in his own thoughts, fails to hear him. Undeterred, Tang decides to take the hammer anyway.
On his way back home, fate intervenes as Tang stumbles upon the same drunken patron, now slumbering peacefully on the streets. He spots the companion nearby and attempts to inform him about his friend's condition. Initially, the companion brushes it off as inconsequential, but Tang's insistence prompts a violent altercation. A haunting flashback engulfs Tang's mind, revisiting a darker chapter of his past where he and Gyeong-hwan were mercilessly bullied by their peers during their high school days.
Tang recounts a life where retaliation was an alien concept, yet on that fateful day, he deviated from his usual path. We witness him extracting a hammer from his satchel and delivering a fateful blow to the man, who crumples to the ground, lifeless. Tang's concern is palpable, yet he retreats into the shadows as pedestrians blithely stroll past. Among them, a blind woman accompanied by her loyal dog, Rex, passes unnoticed, oblivious to the drama that just unfolded.
Back at his abode, Tang hastily scrubs the telltale traces of blood from his skin under the cascading water of the shower. His mind plays tricks on him, conjuring visions of the deceased man mourning the plight of his family. Later in the night, Gyeong-hwan stumbles into Tang's home, his senses dulled by a night of heavy drinking. Their conversation drifts to their high school tormentors, who, ironically, are now thriving in life.
Tang delves deeper into his past, confessing a time he betrayed his girlfriend's trust. He feared discovery but somehow slipped through the cracks, as he had done before when he pilfered Gyeong-hwan's tablet during their school days. It seems Tang possesses an uncanny ability to evade consequences.
Suddenly, reality bites as Tang realizes he's left the incriminating hammer on the street—a direct link to the crime. The following morning, Detective Jan Nan-gam, joined by his colleague Yong-jae, inspects the body, now joined by the lifeless form of another man, Kim Myeong-jin, found in an unrelated location. Meanwhile, Gyeong-hwan hastily exits Tang's residence. Tang, summoned to work at the convenience store due to a colleague's illness, finds himself at the center of an investigation when Nan-gam arrives, inquiring about security cameras.
Two mischievous boys find themselves in Nan-gam's crosshairs, earning a trip to the police station and a stern warning. As the detectives scrutinize security footage, they grapple with the mystery of how the bodies ended up in disparate locations.
Nan-gam, having witnessed the footage of the intoxicated individual purchasing items from Tang, eagerly awaits his arrival at the shop, ready to grill him. As Tang steps in, Nan-gam poses a question, inquiring if he recalls the two gentlemen from the tape. Just when Tang is on the verge of responding, Yong-jae cuts in, disclosing that a witness has attested to witnessing a fight between the two. Coupled with additional test results, they deduce that the men ultimately met their fate through mutual combat.
While scrutinizing the security footage, Nan-gam notices an opportune moment when a fly conveniently obscures the camera lens, precisely during the time Tang retrieved the hammer. The inebriated man's spouse then offers her testimony to the authorities, detailing how her husband frequently hosted Myeong-jin, a colleague, who was charming and considerate. Their affair blossomed, and she even contemplated marrying him. However, Nan-gam remains skeptical about Myeong-jin, as he cannot uncover any records pertaining to him, and a vague sense of familiarity lingers.
Nan-gam revisits the store to purchase chewing gum, using the opportunity to caution Tang about the perils of trauma. He expresses empathy towards Tang, noting their shared burden of having unusual names and enduring similar hardships. Soon after, Gyeong-hwan enters, mentioning his repeated attempts to contact Tang. He reveals that both he and Mi-young were questioned by a detective regarding Tang. The two men subsequently exit for a drinking session.
The following day, Kim Myeong-jin's identity is exposed as entirely fabricated. His true name is Yeo Bu-il, a suspect in a notorious serial murder case dating back to 2009. The police uncover this truth through DNA analysis. Tang, too, learns of this revelation and appears somewhat relieved. However, while engaging in intimate relations with a woman, he hallucinates Bu-il once more. This time, he confronts the apparition with accusations of his own deeds, confident that he had thwarted Bu-il's sinister endeavors.
The narrative shifts to a blind woman, joyfully interacting with her dog within her home. On a table, the hammer utilized by Tang rests, a silent testament to the tumultuous events that have unfolded.
