"Hamamura Nagisa no Keisan Nooto" (Hamamura Nagisa's Calculation Notes) volume 7 by Aoyagi Aito. This volume features impossible problems and how to solve them, also negative numbers, natural numbers, and birthday paradox.
First chapter starts with negative numbers, including basics of addition and multiplication. The math part is about as basic as it gets and probably targeted more at younger readers, but everything else around it were carefully arranged to form an interesting hostage rescue scenario. Most of this chapter is intended to gently setup plot devices to be used in later chapters, one of which is Delos' cube, one of the classic problems in Greek mathematics.
This book then went on incorporate the problems of squaring a circle and trisecting an angle into a murder mystery. Nagisa provided the classic background on how these problems are impossible using only straightedge and compass, then went on to solve the problems through other means. The feeling of reaching the solution to what appears to be an initially impossible problem is similar to those locked-room murder mysteries, except in this chapter, readers find multiple solutions to classic problems and a locked-room murder mystery at the same time. It was a real highlight.
Later chapters includes vivid explanations of how the birthday paradox works, and how Descartes presented solution to the Apollonian gasket as a birthday gift to Elisabeth of Bohemia. This is followed by an army of terrorist samurais who followed the Peano axioms. These didn't quite have the punchline of the earlier impossible problems, but the fact that these topics can appear together and still form a coherent plot is amazing in itself.
There were a bit more development on the terrorist organizations, including some backstory to soften the previous extremist image of the terrorist leader, but perhaps those details aren't important as long as the terrorists can create new problems that keep this novel series going. This volume ends with a cliffhanger math riddle that did exactly that. Looking forward to the solution in the next volume.
Previous (2017-06-11): "Imouto sae Ireba Ii" volume 7 by Hirasaka Yomi
Next (2017-07-16): "Biburia Koshodou no Jiken Techou" volume 7 by Mikami En