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 11

This episode starts right away with the results of the second round of poker where Reiko has 3 queens, Nina has a pair of jacks, Sayuri has a pair of 9s, but Kazuki has a lonely 8. Reiko wins the second round. Team Nina feels very defeated at the moment. How can they win at this rate?

Nina knows that their approach of trying to win with 2 pairs is not working. She knows that they need Kazuki to pick a card that either matches Nina's or Sayuri's cards. Reiko discards one card. 

Nina then realizes that the suit of the card (hearts, spades, diamonds or clubs) is just as important as the denomination of the card. They would have the highest chance to get a flush if they all have cards from the same suit. Nina discards a 7 of spades and king of clubs. Nina then picks up 2 cards, from her face, it looks like she's got 2 cards from the same suit. Sayuri tries to figure out why Nina would discard both cards, and comes to the conclusion that Nina is aiming for a flush. Sayuri discards a 7 of diamonds and looks at Nina for reassurance. Nina nods and says to herself that they are going for a flush of hearts. Nina and Sayuri both stare down at Kazuki hoping he'll understand, but Kazuki ends up changing cards in panic.