Akari drew spell cards from her past investigation cases, and Yuzuru was a lot stronger than she was half a year ago, but in the end, both teams emerged triumphant.
Iku used some kind of device to force Yuzuru's possessor out into the open: The tengu troublemaker Yae Miyagihara!
Now the teams head off to join up and defeat Yae, with Iku emphatically suggesting a coverup so that word of tengu stealing kappa tech doesn't reach the factions.
"Danmaku of Twenty Faces" = The Fiend of Twenty Cases, the first adventure of Akechi Kogoro
Unsolved Mystery "Logic Bomb" = Logic Bomb, a young adult murder mystery by an author whose name escapes me