This is the continuation of the summary of the first Owarimonogatari Volume and contains the chapter "Sodachi Riddle" and starts right where "Ougi Formula" left off.
Again, this obviously contains spoilers.
After having found out that Sodachi came back in Ougi Formula, Araragi tries to confront Sodachi but it turns out that she still hates him, even more than before.
She tells him that she hates all the people who made him happy, despite hating people who are unhappy.
Her hatred towards Araragi seems borderline insanity.
She confuses him further by talking about her locker from 7th grade and eventually retaliates to violence by stabbing his hands with a pen. Senjougahara enters the stage and starts a fight with Sodachi and eventually knocks her out. Note, Ougi Formula and Sodachi riddle take place after Nekomonogatari: Shiro and before Otorimonogatari. This is with Senjougahara already being rehabilitated.
Senjougahara and Sodachi are absent from school the next day and Araragi is trying to figure out why Sodachi hates him so much by investigating the locker she mentioned the day before. Ougi accompanies him again and they find out that the locker belonged to him. Inside of it are three letters envelopes labeled as A, B, and C and addressed to Araragi. This causes him to remember another event he totally forgot about (Nisio much), from back when he was in 7th grade.
Envelope "A" claims that "envelope "B" is wrong, do you want to choose "C"?". Araragi recalls the Monty Hall Problem and figures that his best choice would be "C" rather than "A". Envelope "C" contains a map leading to an abandoned house which he used to called a haunted house and Araragi decides to tell Ougi what this all is about.
We already know this from prior stories, back in 7th grade, Araragi started being behind in school and couldn't keep up anymore, especially in math class. One day he found three envelopes exactly like the ones he just found together with Ougi, also leading to the same house they are at now. The door was opened to him by the a girl living inside and she invited him in to study math. She was the one who introduced the Monty Hall Problem to him and explained the meaning of the envelopes. This made Araragi excited and he started to get interested in math. She eventually offered to introduce him to more math problems like this and teach him everyday at her house. Which he ended up accepting and so he visited her everyday to learn about math.
She never asked for anything in return from him except to never stop loving math, to never ask her about her name and to not to tell anyone about their meetings.
One day Araragi came to the abandoned house to only find an empty envelope taped under a table with no whereabouts of the girl.
Araragi now realizes that girl must have been Sodachi and that she is responsible for turning Araragi into who he is now but he was completely unable to recognize her when they met during their freshman years (the Ougi Formula story of the past timeline).
He is still unable to figure out the reason of Sodachi's disappearance and so Ougi decides to help him again...
Ougi claims that Araragi's memory has been altered or distorted (couldn't figure out the meaning here), and that his memory of the abandoned house is false. She proposes the idea that it was in fact Sodachi's home which looked messed up like that in his memory because of domestic violence taking place in it. Ougi also suggests that Sodachi actually wanted Araragi's help in ending the domestic violence. Sodachi knew that his parents are police officers and was hoping that he would report it to them, with the reason that if she reported it herself, she'd be the one responsible for separating her parents.. Ougi deducts that the reason for Sodachi's disappearance must have been that her family situation got worse.
Sodachi was desperately hoping for Araragi to help her but was let down which resulted in her immense hatred towards him, and probably the fact the he didn't recognize her later. Araragi realizes that he let Sodachi down, while he gained a talent for math from this whole incident and Sodachi got nothing out of it.
Sodachi Riddle ends with Araragi deciding to apologize to Sodachi.
Since this is just the continuation of Owarimonogatari Joukan, there's not much to add other than that Araragi is an idiot and Ougi is a wizard.
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