Ep 10. The Girl Genius' Challenge

Tomoya and Nagisa are on the school grounds when they bump into a small girl named Rie Nishina. Rie is a genius living up to her full potential, with an incredible talent for mathematics. But she's also incredibly lonely and introverted. She likes to calculate the dates of upcoming events and devises a scheme to challenge Tomoya, Nagisa, and all her classmates to guess the correct date of the next student council election. She's wagering a considerable amount of money and the chance to be Nagisa's friend if anyone can beat her.

After a few days, several students, including Tomoya, have successfully guessed the correct date, though all of them have forfeited their guess in favor of Rie, as they don't want to take money from a delicate little girl. But Tomoya is curious about why Rie wants to pay for friends, and about why she acts the way she does. He spots her wandering aimlessly through the halls one day, and approaches her to ask her about her behavior. She tells him that she has problems with friendship because she never really learned how to socialize properly, as she was too busy studying advanced math. Tomoya listens intently, and then decides to help her.

He begins by taking her to the music room, where he plays a song for her. Rie is overwhelmed by the beauty of music and starts to weep. Tomoya smiles and tells her that something like this is what real friendship is all about; sharing experiences, feelings, and emotions. He invites her to join him and Nagisa for lunch, and slowly but surely, Rie begins to come out of her shell. Nagisa and Rie hit it off immediately, sharing stories and laughing together. Tomoya looks on with a sense of pride. He thinks about how much he enjoys helping others, and realizes that he's no longer in it just for himself.

As lunch winds down, Rie tells Tomoya and Nagisa that she has one more challenge for them. She presents them with a math problem involving a box, a rope, and the height of a tree, and challenges them to solve it. While they struggle, Rie is beaming with excitement, happy to be engaging with others. Then, out of nowhere, Fuko runs in, exclaiming that she has solved the math problem. Rie is shocked, as Fuko is a bit thick-headed and not particularly good at math. But Fuko explains that she had a dream where a strange girl taught her how to solve the problem, and that's how she got the answer. Rie is amazed and grateful, and Fuko explains that she's happy to have helped, as she learned a lot from Rie about math and logic, something she's not particularly good at.

As the day winds down, Tomoya reflects on the day's events and the effect it has had on everyone involved. He realizes that not only did they help Rie, but Rie helped them too, as she reminded them of the joy that comes from learning and sharing with others. Tomoya says goodbye to Nagisa and Rie, and heads home, full of hope and optimism. He knows that he has friends that will always be there for him, and he's proud to have been a part of Rie's journey towards friendship and learning.