The school adventure story revolves around Kaito, a puzzle-loving freshman at the private high school named "Root Academy." He is selected as a candidate for "Phi Brain" for his extraordinary mental skills. One day, he and his childhood friend Nonoha tackle the "unsolvable puzzle" hidden in the underground ruins near the school. They are guided by the mobile device given to Kaito by the student council president.

The puzzle is the "philosopher's puzzle," a life-threatening creation of a mysterious intelligence group known as "POG." When he defeats the puzzle, he is designated as a "Solver." Together with Nonoha and other Solvers, Kaito battles POG at "philosopher's puzzles" all over the world.