The Sage smiled kindly. "The answers are not something you find, Alex. They are something you earn. To leave this place and finish your homework, you must pass through the Three Gates of Calculation."

With a sudden jolt, Alex found himself back at his desk. The rain was still tapping against the window. He looked down at Exercise 452. The numbers didn't dance anymore. They stood still, waiting for him to organize them. He picked up his pen and began to write, his hand moving with a confidence he had never felt before.

Suddenly, his computer screen flickered. A mysterious website appeared, titled The Vault of Vilenkin . It promised the ultimate GDZ for the 5th-grade workbook. But as Alex clicked the link, he wasn't met with a PDF. Instead, the room began to spin, and he felt himself being pulled into the glowing monitor.

When he finally finished the last page of his workbook, he didn't look for a website to check his answers. He knew they were right, not because a screen told him so, but because he had built the logic himself, brick by mathematical brick.

"Welcome to the Dimension of Logic," a voice boomed. Standing before him was a tall man with a long white beard shaped like a division symbol. He wore a robe covered in equations. It was the Great Sage Vilenkin himself.

When Alex opened his eyes, he was standing in a world made entirely of graph paper. The sky was a pale blue grid, and the trees were shaped like isosceles triangles. In the distance, he saw a majestic castle built from giant wooden rulers.

The second gate was the . Here, the trees spoke in riddles. "If a cyclist travels at 12 kilometers per hour and has a 30-minute head start..." Alex didn't panic. He pulled out a stick and drew a diagram in the dirt. He calculated the meeting point with precision, and the thorny vines parted to let him through.

The first gate was the . To cross it, Alex had to simplify a series of complex fractions that blocked his path. Each time he correctly divided the numerator and denominator by their greatest common divisor, a section of the bridge lowered. He worked quickly, remembering his lessons about prime numbers.