Suugaku Joshi Gakuen Ep 12

It's the final episode. What does everyone think about math now?

Nina is confused why her sister, Machida Kina, is here. Kina explains that she's here to fight Nina. Kina explains to Kazuki and Sayuri that Nina came to this school to find Kina and find out what happened to her after she became Math Boss. Nina is still confused and Kina says that she wants to rule over all the mathematicians in the world. (What? Why?) Kina wants to wipe out all the math schools using her position as Math Boss, even this one. Kina didn't want any mathematician to get in her way of ruling the world.

Nina is in shock. The sister she knew would never act like this. She would be so happy and excited about math, but the person she's looking at has dead eyes. Kina says it looks like she has to fight Nina and destroy her. Nina accepts the challenge and will defeat this impostor. Kina is so confident that she'll win that she tells Nina that this will be her last battle.

Team Nina and Kina are in a classroom, where Kina explains that the book she's holding holds 1200 years of math history, including 20,000 math problems that have been unsolved during all those years. Kina says that she'll choose a random unsolved math problem and Nina accepts. The problem Kina chooses is "Clearly prove that 1 + 1 = 2". Kazuki comments saying that everyone knows that answer is correct, but how would you go about proving it.

Suugaku Joshi Gakuen Ep 4

Onwards to a review of episode 4!

In episode 4, it starts out with Nina freaking out because she can't find her mentaiko bread and accuses Kazuki of stealing it (ah yes, the Kazuki accusations never end). Of course, Kazuki didn't do it and they both end up yelling at each other until Aoyama Iroha (played by Kikkawa Yuu, Hello! Project Egg graduate and is now currently a soloist under Universal Music Japan, but still part of Up-Front, the company in charge of Hello! Project), who is the head of the Morality Squad, tells them to stop fighting like kids and that Kazuki should cut his hair because it's not manly and supposedly long hair on a man is against the school rules. Kazuki is scared and freaked out, but Nina continues to be angry and badmouths Iroha. 

Kazuki is so mad at Nina that he heads over to the old school building, and notices Sayuri in the building. He tries to creep away, but steps on some leaves and Sayuri notices him, but didn't notice that she noticed and  keeps walking. Sayuri had eaten some of Nina's mentaiko bread and it gave her a stomach ache, causing her to need to do a #2 and she finds it too un-idol-like, which is why she is at the old school building, so she can do her business without anyone knowing. Kazuki ends up writing a whole bunch of mean things on the blackboard about Nina to vent out his anger. Kazuki, in the classroom, and Sayuri, in the washroom, both hear the sound of a window breaking. 

The next day, the class is assembled to bring up the fact that a window had been broken in the old school building, an indication that it must have been vandalized. Two girls quickly point out that Sayuri and Kazuki were both at the old school building. Mami senses that this is a case and decides to handle it, until Iroha gets the other 2 members of the Morality Squad to drag Mami out. Iroha, who is now in charge, asks Sayuri and Kazuki why there were at the old school building, but neither one of them want to say why because Sayuri doesn't want anyone to know that an "idol" like herself uses the washroom, even more so does a #2. Kazuki doesn't want to say anything because he technically did do some vandalism and doesn't want anyone to find out what he wrote on the blackboard. Iroha assumes their silence as being guilty. Nina stands up for them saying that there was no way that they did it. Kazuki and Sayuri both appreciate the sentiment, but they are in this predicament because of Nina. ^_^"  So, Sayuri and Kazuki are both placed in separate enclosed rooms and are forced upon the "Prisoner's Dilemma", where accusing the other will cause them less consequences than staying silent.