The Boy Genius' Melancholy (天才少年の憂鬱 Tensai Shōnen no Yūutsu) is the third episode of Phi Brain: Kami no Puzzle Season One and the third episode of the anime series overall.
Kaito meets a boy genius solver named Cubic Galois, who carries the title of 'Edison' and prefers mathematics over puzzles. He attaches a strange bracelet onto Kaito's arm, which causes his head to hurt whenever he thinks about puzzles. At this time, Kaito, Nonoha and Gammon are called to solve a puzzle, with the city rigged to explode if they fail. Though Cubic tries to make things harder for Kaito to make him give up on puzzles, he soon learns that the puzzle giver is serious about blowing up the city. With less than two minutes remaining, Kaito enters his Phi-Brain state and solves the puzzle with a second to spare. Admiring his skill, Cubic apologizes to Kaito and removes the bracelet.
Following the events of the previous episodes, Kaito asks the Principal why he receives puzzle invitations from the device. Kaito walks out of the room when he did not get his answer. Nonoha tries to convince him to quit solving Sage Puzzles when another title-holder Cubic Galois, who holds the title "Edison", agrees with Nonoha, and invites them to his laboratory in Root Academy. Kaito becomes disinterested and left the room with Nonoha. However, Cubic kept following them until he had the chance to place a "charm against puzzles". Cubic places a bug on him right before he receives another puzzle invitation. When he tried to solve the invitation code, his mind restricted him from doing so and hurts him. Gammon instead solves the code and they go to the said location. There they meet a POG Giver. If they didn't solve the puzzle in 16 minutes, a bomb would explode and destroy the city. The first puzzle given is a sudoku, where the katakana letters would spell the location of the next puzzle. Kaito tries to solve it again, but the same thing happens with the invitation code. Cubic appears to tell them that the wristband disrupts Kaito's thinking when he tries to solve a puzzle. Additionally, Cubic removes some numbers in the sudoku that makes it harder, but still solvable. They solve the puzzle that convinces them to go to the park. The POG Giver instructed them there to find the 16 numbers hidden in the park. They found a couple, but the park was too big. With three minutes left, Kaito breaks the wristband on the ground and he enters into Phi Brain state once more. He figures out that the puzzle was a 4x4 magic square, where the sum of the numbers in each row and column was equal to 34. The numbers were naturally 1-16. 20 seconds was left for Kaito to solve the puzzle and input the numbers. He finishes again with one second to spare, and all three of them faint, the other two from anxiety and Kaito from exhaustion. The POG Giver refused to lose and tried to detonate the bomb, but POG has already defused the bomb and they removed the giver from his position.