Keizoku/Manga

Graduating at the top of her class, elite detective candidate Jun Shibata is transferred to the section that handles cases deemed "unsolvable" by the department. Her partner, though a well-respected and experienced detective, has grown complacent after unsuccessfully pursuing these cases that many consider an exercise in futility. With her upper class breeding, her colleagues don't expect much from her either, but she suprises them all with her motivation and astounding powers of deduction.

(Source: Asian Wiki)