Phi Brain: Puzzle of God

Whilst exploring a Sage's Puzzle in England with Jin in the hopes of recovering his memory, Kaito stumbles upon an unsolved puzzle, having assumed Jin had already solved all of them. Solving the puzzle with ease, Kaito discovers a brooch with a cat engraved on it, which Jin takes an interest in. Later, they, along with Nonoha and Rook, go to the Fool's Puzzle where Kaito and Rook previously faced off against each other, where they encounter a strange girl named Raetsel, who takes the brooch and runs off with Jin inside the puzzle, activating its traps. Back in Japan, a man named Johan Seigmund Enigma appears before the other Phi Brain children, attaching an explosive puzzle on Cubic's back, stating his intent to annihilate all puzzlers, claiming it to be Jin's desire. After the bomb is disarmed, Enigma leaves whilst his accomplace, Whodunnit, challenges the others to a puzzle. Meanwhile, Kaito's group arrive at a room with many doors, with Raetsel tasking them with finding the correct door before the ceiling collapses, claiming that Jin hated puzzles.

Thanks to Kaito's deductions and Nonoha's memory, their group manages to find the correct exit and escape. Afterwards, Raetsel takes everyone to her personal boat, where she shows them a feed of Gammon's group as they face Whodunnit's puzzle, where they must arrange cubes successfully or else be electrocuted. Working together, they deduce the colors of the cube are a clue to numbers in a magic square puzzle, managing to solve it with a second to spare. Although Raetsel leaves Jin with Kaito and the others, they are left uncertain by how the Master Brains, who target puzzlers for bounty rewards, claim to be contracted by Jin.

As Raetsel transfers into Root Academy, Gammon spots Jin behaving rather oddly, uncertain whether or not to believe either Kaito or Ratesel. Later, a Master Brain posing as Jin appears before Kaito, challenging him to a Fool's Puzzle in which he much navigate a sliding puzzle maze within a time limit or else fall to his death. As Kaito comes close to solving it, the fake Jin blows out one of the rooms, preventing him from reaching the exit, as well as tilting the maze. However, Kaito manages to take advantage of risky nature and reach the maze's goal in time.

Whilst Kaito is having a picnic with Jin and Nonoha, Raetsel appears before Kaito, stating that the Fools' Puzzles made Jin suffer, clashing with Kaito's own memories of him. However, Nonoha helps them realise there are some memories of Jin that they both share. Meanwhile, a Master Brain named Dr. Theorem appears before Cubic, who decides to face him in a puzzle to prevent him from reaching Kaito. Cubic is tasked with finding 'the most beautiful number' within 15 minutes before he is engulfed in flames. After Kaito learns of Cubic's predicament, he rushes to his aid and helps him find the solution; the golden ratio. After the battle, however, Jin starts experiencing pains in his head.

Rook calls Kaito and Raetsel together, telling them about a time he had a talk with Jin, who told him a cryptic message about puzzles being both 'chains' and 'mirrors', which he had also told Raetsel. He goes on to explain his research on Jin's year spent with Raetsel, showing that even though he fought against Fool's Puzzles, he also taught others the fun of puzzles. Wanting to prove her own case, Raetsel takes Kaito and Rook to a Fool's Puzzle that Jin wasn't able to solve, consisting of various elevators above a bottomless pit. Seeking an answer to Jin's riddle, Rook takes on the puzzle, in which he must navigate the elevators based on their assigned numbers or else be crushed. With encouragement from Kaito to listen to puzzle's voice, Rook manages to reach the goal. Rook states he was able to solve the puzzle thanks to a clue allegedly left behind by Jin, who apparently lied to Raetsel about not completing it to keep her safe. Rook then states his answer to Jin's riddles, that puzzles are both chains that link people together and mirrors that reflect the solver's emotions.

Elena, who had just come back from abroad, becomes curious about Raetsel and decides to hold a welcoming party for her to find out more about her. This attracts the interest of Ana, Airi and Tamaki, who all invite Elena to hang out with them, hitting the shops before going to a pool. Meanwhile, Gammon, who becomes irritated that his bounty is lower than the others, is called out by a Master Brain named Colonel Demolitionman, who traps Elena's group, along with Kaito and the others, inside the pool building. This puts pressure on Gammon, who has to solve a set of puzzles from inside a tank before it smashes into the building with everyone inside it. Despite facing up against great odds, Gammon's determination to not lose lets him solve the puzzle and stop the tank in time. Afterwards, Raetsel confronts Enigma, who put her at risk as a reminder of her mission. As Raetsel chooses to break her new ties of friendship and go back to her old self, Melancholy is seen with Raetsel's group.

Rook informs Kaito that Jin had previously made some Fool's Puzzles, which he himself destroyed as a means to improve his Giver skills, theorising that he may have been under influence from the Orpheus Bracelet. Kaito, refusing to acknowledge this, shows Jin a warm puzzle he once showed him during his childhood. Meanwhile, Freecell falls into a trap laid out by Melancholy, who has joined the Master Brains in order to get revenge on him, trapping him in an underground maze. Learning of Freecell's predicament from Pinochle, Kaito, Nonoha, and Gammon fly to England to search for him, finding him at an old train yard, where Melancholy challenges Kaito, Gammon and Freecell to a Fool's Puzzle, in which they must connect with their partners whilst sacrificing the other players. Contrary to her expectations, however, Melancholy is chosen as the fourth player in the game by Enigma, who had caught onto her intention to try and save the others and also claims it to be a puzzle built by Jin. As Gammon notices a message laid out by Kaito, both Freecell and Melancholy struggle with theirs.

Freecell and Melancholy soon come to understand Kaito's message, allowing the four of them to reach a solution that allows everyone to escape alive. Afterwards, Melancholy invites everyone to her mansion for dinner, where she lives alone with her maid and butler. Later that night, Kaito and the others come across a room filled with puzzles Melancholy made for her Master Brain training, which helps Freecell rekindles his love of puzzles. Still holding onto her hatred, Melancholy burns all of her puzzles. The next day, however, the others come across her feeling remorse, realizing she made puzzles because she was lonely, and ask to become her friends, to which she stubbornly declines. Not wanting to give up, Freecell asks Kaito to design a crossword puzzle for her to solve after they leave, saying they will meet again. Meanwhile, Raetsel suspects something is up with Enigma.

Baron, Souji, Rook, Bishop, Raetsel, and Jin are all called up to meet up with Enigma to discuss Jin. Enigma talks about how Jin first met Raetsel, noticing her skills in crafting puzzles, and took her on his journey to protect her from organizations like the POG. When Raetsel discovered Jin was going up against Fools' Puzzles, she believed he was suffering alone and resolved to help him. Eventually Jin left Raetsel to go up against Count Pythagaras, where he lost his memories. Enigma claims that Jin told him to assemble Master Brains and annihilate all puzzlers should something happen to him, though Souji remains suspicious about whether Enigma has his own agenda against puzzles. Meanwhile, Raetsel states Jin told her she could abandon puzzles should she choose, which Jin does recall saying. Afterwards, Rook and Souji believe there may be clues in God's Puzzle and God's Scripture on how to restore Jin's memories. Meanwhile, Baron questions Jin on what he told Raetsel, since it contradicted what he once said to Kaito, which Jin suspects may pertain to something Kaito has that Raetsel doesn't. Raetsel, who had overheard them, remains in denial and takes Jin for herself, challenging Kaito to try and find them.

Following a hint Raetsel left them, Kaito, Nonoha and Gammon travel to Texas, where they meet a girl named Nono and her brother, Joe, who is a skilled basketball player. Nono explains that Joe was scouted for a pro team, but when their parents died, he quit basketball to take over his father's job, which is revealed to be as a Master Brain. Joe challenges Gammon to a Fool's Puzzle, in which they must race against each other through a maze left behind by his father, using bikes that have had their brakes cut. Despite being cut off from the latter half of the maze, Gammon manages to use the maze's walls to get ahead of Joe and win the race. Afterwards, Gammon reminds Joe to follow his true dream and take up basketball again, whilst Kaito finds a clue in the maze's center directing them to their next location.

With Kaito's group stuck between flights, Cubic and Ana go ahead of them to Rio de Janeiro, where they meet a woman named Regina Maria Vasco. Taking them to a hidden cave under the pretense of helping them find Raetsel, Regina reveals herself to be a Master Brain and traps Cubic and Ana in a Fools' Puzzle, in which they must travel via canoe across several containers whilst making sure they end up with equal volumes. Cubic makes some progress with his calculations thanks to Ana, but Regina keeps interfering with their progress. Luckily, Cubic's robot, Iwashimizu, arrives and uses a stalactite to bring the water up to the right level, solving the puzzle and earning their next clue. As Kaito's group finally arrive only for the puzzle to be already solved, Herbert is seen talking to Enigma.

After discovering some puzzles in South America, along with a ring left behind by Raetsel, Kaito's group soon come up against Herbert, who has equipped himself with four replica rings. He challenges the group to use their own weight to determine a balancing puzzle. After some initial confusion, Kaito manages to figure out the puzzle's hidden gimmick and solve it. As Kaito urges Herbert to throw away the rings, Herbert finds himself at odds with his own conscience, eventually finding the power within himself to break free of the rings. After Herbert inadvertently sets his own trap on himself, the group head towards the Andes.

Feeling that she somehow needs to prove herself to Jin, Raetsel decides to confront Kaito herself, challenging them to find Jin inside a Mayan pyramid. Meanwhile, Rook and FreeCell arrive at an Egyptian pyramid where the Pythagoras Scriptures are believed to be hidden. As Kaito travels through Raetsel's puzzle, he feels that it is shallow and half-hearted. Upon reaching the maze's center, Raetsel questions if Kaito will be able to accept whatever truth lies before him, Kaito echoes what Jin taught him about not running away from the truth. However, the Jin at the center of the maze turns out to be the impostor Jin from before, with Raetsel trapping Kaito and the others inside the maze, holding them as the prize for Rook and FreeCell's puzzle.

Rook and FreeCell is tasked with helping each other get through the pyramid's maze using hieroglyphic gateways within ten minutes before they are locked inside forever. Whilst they quickly figure out the relationships of which gates open up with other, they soon find themselves at a dead end. Freecell suggests that they stop thinking like Solvers and instead think like Givers, deducing what methods Raetsel would use to keep them trapped inside, discovering the puzzle's weakness and arriving at the center of the maze in time. As Enigma sets the two pyramids to self-destruct, Rook and Kaito discover switches in both pyramids which reveal the Pythagoras Scriptures, before they escape safely. Meanwhile, Enigma forces Raetsel and Jin to flee from their hideout, hoping to push her into a corner.

While the Baron is revealing Jin's past and his ties to the fallen puzzler Lavoushka. Enigma shows up and reveals his past and his motives for having the puzzlers eliminated

Kaito and the others arrive at Raetsel and Jin's location, where Kaito and Nonoha decide to speak with Raetsel privately, telling her what they learned from Enigma. Raetsel states she had apparently figured everything out herself, telling Kaito that Jin's memories will return if they face off against each other by a 'Killing Colloseum' puzzle that he and Raetsel made together. The puzzle soon begins, in which they must try and reach an exit before their opponent whilst avoiding deadly boulders. Although Kaito tries to get the puzzle to end in a draw so they can both escape safely, Enigma suddenly appears and brings Jin to the center of the puzzle. As Kaito and Raetsel rush to his aid, Jin regains his memories, allowing him to lead the two safely out of the puzzle via an escape route he had built. However, upon exiting the puzzle, they discover that Jin has been possessed by someone calling himself the Phi Brain, Orpheus.

After Kaito, along with Raetsel, Rook, and Freecell, once again sees the vision of a ruined future, Orpheus demonstrates some of his power on Kaito, temporarily showing him an illusion where he failed to rescue Raetsel from the puzzle. Tempting him with the possibility of bringing Lovushka back to life, Orpheus gets Enigma to join his side and the two escape. The next day, Rook and Freecell explain their findings, explaining Orpheus transferred his mind into Jin's body during his battle with Pythagoras, and the scriptures were just a lure to bring people to the Puzzle of God. It is then revealed that Jin himself locked away his own memories in order to suppress Orpheus, and the power Orpheus used on Kaito was an incomplete ability to alter time. Just then, they receive a call from Raetsel, who had decided to join Orpheus as well, saying the only way to save Jin's mind is if either she, Kaito, Gammon, Rook, or Freecell awaken as a Phi Brain and offer their mind to him. As Kaito becomes angered by Rook's suggestion to either find an alternative way of saving Jin, or else kill him to protect the world, Freecell suggests to Kaito that if he can become a Phi Brain before Orpheus, he may able to save the future. Accepting this channel, Kaito heads off with Freecell and Nonoha to Amigne, where Orpheus awaits. Upon arriving, they are shown a vision of Kaito and Nonoha's childhood.

Orpheus appears before Kaito and the others, showing each of them alternate versions of their past, including Kaito managing to save his parents and Freecell's mother never having the Orpheus Ring. He then shows a genuine look at Nonoha's past where, even though a fit of binge eating left Nonoha unable to solve puzzles anymore, she still felt joy in seeing Kaito solve puzzles. Orpheus then reveals he made the bracelets to determine worthy vessels for his power, tempting Kaito and Freecell with the offer of becoming Phi Brains so they can change the past, in exchange for Jin's safe return. However, Nonoha knocks some sense into them, reminding them that both the good and the bad things of the past are what made them who they are today, letting them turn down Orpheus' offer and return to reality. Meanwhile, Jin regains temporary use of his body due to Orpheus stressing too much of his power, telling Raetsel he intends to let Orpheus die with him. As Gammon and Elena head towards Amigne themselves, Kaito and the others arrive at Orpheus' puzzle.

Whilst Kaito's group tackles the puzzle before them, Gammon and Elena meet up with Raetsel in Amigne, eventually coming face to face with Orpheus, who brings them to an illusionary Sage Puzzle with an Orpheus Bracelet up for grabs. Tasked with navigating a sliding puzzle within a time limit, they soon hit a snag when some red panels thought to take them upwards through the maze take them down instead. However, Gammon eventually manages to find the puzzle's secret and reach the goal in time. Returning to the real world, Gammon finds he is now wearing an Orpheus Bracelet, but manages to resist its power and break it with his sheer stubbornness to be better than Kaito. Later that night, as Gammon gives his thanks to Elena for her help, he sees a vision of the future.

Told by Orpheus that she won't be able to become a Phi-Brain as she is, Raetsel agrees to take on a Sage Puzzle in order to obtain an Orpheus Bracelet. Despite Jin's objections, Raetsel enters Orpheus' world to a maze, in which she is only allowed to climb downstairs. During the puzzle, Raetsel sees visions of her past with Jin, desiring the power to change the past so she can stop him from facing up against Pythagoras. Some time later, Raetsel, along with Kaito and Rook, see another memory in which all three of them spent time with Jin, which Rook believes isn't simply an illusion. After figuring out the puzzle's trick, Raetsel solves it and earns an Orpheus Bracelet.

As Souji, Cubic and Ana meet up with the Orpheus Order to learn what they can about Orpheus, Rook, who has received an Orpheus Bracelet from Orpheus, challenges Kaito to a puzzle in which they must race against each other in roller coasters. Rook reveals that Orpheus' ideal is to surpass the gods, stating that he has seen the future that Kaito will fail the puzzle. However, Kaito's determination to save both of them proves Orpheus' future to be false, shattering Rook's resolve. Near the end of the puzzle, though, Rook reveals that the track is designed so only one can escape safely, sacrificing himself to let Kaito escape. This leaves Kaito more determined than ever to become a Phi Brain and defeat Orpheus.

Called together on a yacht by Enigma, Kaito, Gammon, Freecell, and Raetsel participate into a block-pusing maze puzzle to decide which two shall take on the Puzzle of God. Raetsel is the first to reach the center of the maze and escape after outwitting Freecell, with the remaining players now having to face explosive walls. Kaito and Gammon also manage to open the way to the exit, but Gammon becomes trapped under some rubble, with both Gammon and Freecell urging Kaito to not hesitate and escape on the last escape pod as Enigma sets the yacht to explode.

After Orpheus informs Kaito and Raetsel that they'll be facing the Puzzle of God the next day, Kaito tells Raetsel not to come as he doesn't want anymore casualties. As Kaito shuts himself away whilst the others arrive in Amigne, Baron assures them that Gammon and Freecell made it out of the yacht okay, though he later tells Souji that this is just a lie to keep them from stopping Kaito from solving puzzles. Later that night, Raetsel takes Kaito to a festival, helping to realise the reason what he is fighting for and return to his energetic self. With the two deciding to challenge the Puzzle of God, Kaito and Raetsel return to the others, where Raetsel is invited to spend time with the other girls. As Raetsel feels thankful for the night of fun she had, she manages to break her Orpheus Bracelet. The next day, Kaito and Raetsel arrive at the Puzzle of God, a giant territory based puzzle game that is linked to their very past.

As Kaito and Raetsel are shown their pasts, which change based on their hearts' desires, they overlap, showing a vision of Kaito joining Jin and Raetsel on their journey. Upon reaching a point where Jin chooses to leave Raetsel behind and take Kaito with him, Raetsel feels dissatisfied and attempts to change the result, repeating the same loop over upon Jin telling her she is 'missing something', until she chooses to reject the memory altogether and end up in a fabricated world where she never met Jin. In this world, she comes across a brooding Kaito and takes an interest in puzzles, until he one day goes missing. After learning from an encounter with Ana that everyone is 'missing something' in some way, she comes to realise that even if she is lacking something, she is still able to have fun, managing to break free from the fake world and rejoins Kaito. Kaito explains he was able to find Raetsel by taking a path he would never take in the real world, a world where he never went with Jin and learned to love puzzles, where he grew to understand Raetsel's feelings. Just then, Orpheus decides to stir things up, separating Kaito and Raetsel.