Thanks for the chapter!
Seems like Luna has some good qualities after all, but seems determined to be free spirited and do things in a way that's sure to agitate others.  Definitely has a good eye for people considering she knew Rintarou could solve the equation although setting him up to trample on the teacher's pride because she couldn't do it herself was really underhanded.  Seems to be a pragmatic results oriented personality who's not picky about means.  Granted really dishonorable compared to the legendary Arthur but is very charismatic, able to attract and lead followers. Also, wouldn't the legendary Arthur be ground to dust from overwork and eaten alive by the corrupt politicians of this era who know how to bend/break or can buy their way around laws, rules, and able to lie with a straight face?  Arthur would be honest, do more than his share to help others, take responsibility for his action and those of his subordinates.  Corrupt politicians would go on the premise of it's only wrong if get caught, experts in passing blame and responsibility to others, take credit for accomplishments done by others, dump hard jobs on Arthur along with blame for failing while embezzling and sabotaging his efforts.
As for Rintarou seems like he went through a lot of pain and grief due to the jealousy of others for his high spec abilities.  That soccer player and student shouldn't have agonized so much over how Rintarou was able to do better despite their efforts, but asked for tutoring to further enhance themselves rather than selfishly stating their best is the limit and Rintarou is a monster for surpassing it.  Granted his talent makes it a lot easier for him but it doesn't mean he couldn't find a way to teach them in a more efficient way that sticks.
@Arcverson  Teacher is more stupid for listening to the nonsense and bullying others rather than learn from his mistakes and try again.  Granted Luna lying was underhanded but she seems a good judge of character and accurately read that he was able to solve the equation.  To me it looked like she was so sure that the possibility of not being able to answer the question didn't enter her head.  Also, while she does come across as arrogant scum, I doubt pride and looks would be enough to become Student Council President, have majority of students support her, or have Nayuki helping her out as treasurer and comment on how Luna is the reason everyone can smile and have fun.