Seok-go (Ryoo Seung-beom) is a quiet and seemingly unassuming maths teacher living alone in a Seoul apartment block. Deeply enamoured with his neighbour, Hwa-seon (Lee Yo-won), he visits the cafe where she works each lunchtime without fail - always ordering the same takeaway food - but, try as he might, his shyness repeatedly prevents him from connecting with her on an emotional level; managing only an almost embarrassed 'hello' and 'thank you' he walks away frustrated and unfulfilled on each occasion.
On hearing a commotion coming from Hwa-seon's apartment one evening, Seok-go knocks on her door to ask if she needs his assistance only to find that she has killed her ex-husband in a vicious struggle and is planning to hand herself in to the police.
Seok-go immediately suggests that, instead, he'll dispose of the body; help Hwa-seon to hide her crime and talk her through any subsequent police investigation.
However, before long questions begin to surface as to the true reasons behind his seemingly altruistic actions...

What would you be prepared to do for love? More than that, if someone told you they "did it for love" would you assume they meant love for someone or love from someone?
From the very moment we are first introduced to Seok-go as he awakens in bed hearing Hwa-seon talking to her niece outside her apartment, director Bang Eun-jin beautifully accents a link between the two main characters - a link initially only existing from Seok-go's point of view - and not only hints at his (too) deep feelings for a woman he barely knows but also foreshadows later revelations without directly stating their existence; thereby allowing for a feeling of hindsight when the true state of play begins to show.

In fact, scenes, narrative elements and character personalities having more to them than first meets the eye really is the order of the day throughout Perfect Number and in terms of Seok-go's persona we quickly learn that a simple maths teacher is far from what he is: For here we have an incredibly intelligent man whose analytical brain can seemingly plan for every variable, on the spot, in any given situation; a man who is utterly convinced that he can out-think anyone and everyone. As such, when he is brought face-to-face with the dead body lying on Hwa-seon's floor, he instantly sees the opportunity to kill two birds with one stone, if you will: By helping Hwa-seon to hide the murder (and her part in it) he's sure he'll be seen to be acting out of love - hopefully making her fall in love with him, in the process - and by meticulously planning for every eventuality that a police investigation may bring he will, at the same time, resolutely prove his superior intelligence and his ability to outwit anyone without even breaking into a sweat.

More than once during the course of the film, reference is made to a classical mathematical theorem that Seok-go has been obsessed with trying to prove since his school days. However, in helping Hwa-seon hide her crime his focus increasingly shifts from a sole preoccupation with the concept of a Perfect Number to a deep-rooted intellectual and emotional need to maintain her alibi and thereby create the perfect murder.
Hwa-seon is, by comparison, a far more straightforward and altogether simpler character. While she could be said to stand as a personification of the idea of single parent families - with her life, it could be inferred, the result of breakdown of the classic 'family unit' increasingly seen in Korean cinema - she serves as much, if not more so, as simply the catalyst allowing Seok-go's numerous character traits (shy and caring to needy and clawing to self-serving, manipulative and worse) to gradually show themselves; in spite of her character's story being at the very crux of the narrative.

This is added to yet further by the third piece in the character puzzle; that of Min-beom (Jo Jin-woong), the police detective in charge of the case who is also an old school friend of Seok-go:
From almost the moment he is assigned to the case, Min-beom is utterly convinced that Hwa-seon is guilty of murder despite there being no evidential proof to be found, and as he re-acquaints himself with Seok-go it soon begins to dawn on him that not only is his high-school friend intelligent enough to bury the truth and provide Hwa-seon with an airtight alibi but also that the challenge of doing so would be almost impossible for him to resist.
Thus, Min-beom unrelentingly continues his investigation of the two, almost to the point of harassment; pushing them to extremes in the process and catapulting all involved towards the climactic conclusion of the tale.

Ultimately, for all his intelligence Seok-go is set to find an answer he didn't even know he was looking for... the answer to the question "In a battle between heart and mind, which will win?"

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Wireframe notes (UI)

DVD

The DVD edition reviewed here is the Korean (Region 3) Art Service Limited Edition First Press version. The film itself is provided as an anamorphic transfer with an aspect ratio of 2.35:1 and there are no image artifacts (and no ghosting) present.
The original Korean language soundtrack is provided as a choice of Dolby Digital 5.1 or Dolby 2.0 and both are well balanced throughout.
Excellent subtitles are provided throughout the main feature but English-speaking viewers should note that, as with many Korean DVD releases, there are no subtitles available on any of the extras.