Lux, a former prince of an empire named Arcadia that was overthrown via a rebellion five years earlier, accidentally trespasses in a female dormitory's bathing area, sees the kingdom's new princess Lisesharte naked, incurring her wrath. Lisesharte then challenges Lux to a Drag-Ride duel. Drag-Rides are ancient armored mechanical weapons that have been excavated from ruins all around the world. Lux used to be called the strongest Drag-Knight, but now he's known as the "undefeated weakest" Drag-Knight because he will absolutely not attack in battle. After his duel with Lisesharte, Lux ends up attending the female-only academy that trains royals to be Drag-Knights.

From MangaHelpers:

There's a new wheel-chair bound student at school who has returned after an illness, and she immediately kisses Tsuzuki Ui, who she calls "Rei-kun." He soon deduces that she is a daughter of a wealthy family, and a person he once beat at an internet murder mystery game. She is apparently fixated on him, since he was the only one who ever beat her, and she has now come to see him in person. Her plan is to have a real-life murder mystery game, and her current focus is on the supposed suicide of Tsuzuki's father. For some reason, she suspects his little sister Haruka... [tethysdust]