fail to solve a puzzle by the time limit. The door has been blocked, and there is no escape. The PDA periodically displays new puzzles. As the occupants of the room work to solve the puzzles, it is revealed that Oliva and Galois have a romantic history, and that Oliva cheated on him with Hilbert. They pile the furniture in the room to hold the moving walls, but the furniture is broken as the walls continue to contract. Pascal identifies the girl in the photo as someone that he severely injured with his car. He proposes that Fermat is trying to kill him in revenge, and that the others are collateral victims. When they discover an invitation addressed to Fermat with different instructions than theirs, they realize that Fermat was not their host after all, but another pawn of the true host; if this is a revenge plot, the person wanting revenge would want to see it happen. As there are no visible cameras or viewpoints, the person trying to kill them must be in the room with them. Galois, who previously gained press attention for allegedly proving Goldbach's conjecture, confesses that he lied to win back Oliva; the publicized sabotage of his presentation was staged to hide his failure. Hilbert reveals that he is the mastermind, that he has spent his entire professional life trying to prove Goldbach's conjecture and was insanely jealous that Galois beat him to the proof; he staged this "convention" to avenge himself. Fermat was a diversion who will be killed when undetectable poison gas is released in his car. Hilbert announces that he has succeeded in proving Goldbach. He hands a folder to Galois. Galois admits that Hilbert's proof is brilliant. Frustrated by their impending doom, Galois becomes angry and strikes Hilbert, rendering him unconscious. Pascal realizes that the real Oliva, Galois, Fermat and Pascal each died at the same age as the current age of the guests using those names, but the real Hilbert died at 81, much older than the unconscious man before them. They conclude that Hilbert had an escape plan and did not intend to die with them. The three find a breakable wall panel and escape with Hilbert's proof. As they return to their cars, Galois is conflicted about releasing Hilbert's solution: releasing it under Hilbert's name would let Hilbert "win", while releasing it under his own name would