A lot of plot development happened in this episode. Rook just outed himself to Einstein as a member of the POG. And that he is in fact the #2 person in the POG with only Pythagoras being ahead of him. There is also the Headmaster of Root Academy and Jigukawa out themselves to Einstein’s friends as members of the POG. But at least it seems that they do not have the same goals as Rook and Pythagoras. That is because they have decided to help Nonoha and the others get to him.
Unfortunately they are a little late to the party because Einstein has already solved the Fool’s Puzzle and almost died because of it. Einstein was pretty smart to kick that saw blade into that lift to open it or else he would have never been able to solve the puzzle. But it makes me wonder how strong Kaito really is because that saw looked like that it was made of some pretty heavy metal. But enough about that. At the end of the puzzle it seemed like Einstein lost all interest in puzzles because of Rook. The one person he thought he could trust and he turned out to be a part of enemy faction.
It seems that Rook has some issues with the way that their Mentor Jin Makata favored Einstein over him. It seems that both that both Jin and Einstein were solvers where as our villain Rook here is a giver, hence why he is part of the POG. It seems that Rook kind of actually wanted Einstein to die in the puzzle because of those existing issues, but he also wanted him to live because he wants Einsteins to develop into a full phi brain. But the only reason for that is because the POG wants to get at the treasure kept in the Puzzle of God. It seems that it is a treasure that would make a person a god. Let’s see what happens there.