The chamber beneath the Tower of Numbers pulsed with a heartbeat Mark could feel in his bones. The equation on the pedestal—2x² + 8x = 0—glowed brighter, its symbols shifting like liquid starlight. Mark's chalk hovered over the stone, his choice between x = 0 and x = -4 hanging in the air. Lyra stood at the edge of the chamber, her slate-gray eyes locked on him, unblinking.
"Choose," she said, her voice low but sharp. "The Tower doesn't wait."
Mark's mind churned. Zero was simple, clean—a reset, a return to nothing. But -4 felt heavier, like a debt unpaid. In Numina's streets, he'd learned that nothing came free; every choice carried a cost. He pressed his chalk to the stone and wrote: "x = -4."
The chamber roared. The equation dissolved into sparks, and a wave of Numen—dark, cold, and heavy—slammed into his Scholar's Seal. Pain shot through his wrist, but he didn't flinch. The pedestal sank into the floor, revealing a narrow bridge over a chasm so deep it swallowed light. Across it, a new archway shimmered, its surface rippling with symbols that looked like fractions and exponents, dancing in patterns Mark couldn't yet read.
Lyra stepped closer, her boots echoing. "Negative four," she said, almost a whisper. "You picked the harder path. Most don't."
"What's it mean?" Mark asked, rubbing his wrist where the Seal burned.
"It means the Tower trusts you to carry weight," she said. "Zero's easy. Negative numbers? They're promises of struggle. Let's go."
The Bridge of Fractions
The bridge swayed under their steps, its surface etched with glowing fractions: 1/2, 3/4, 7/8. Each step made the numbers pulse, as if testing their resolve. At the far end, the new archway loomed, its voice softer but no less commanding:
"To cross, prove you can wield parts of the whole. Solve: 2/3 + 5/6 = ?"
Mark's heart steadied. Fractions were familiar; he'd seen merchants in Numina's markets haggle over portions of grain. He needed a common denominator. Three and six—six worked. Convert 2/3 to 4/6. Then 4/6 + 5/6 = 9/6 = 3/2.
"Three halves," he said.
The bridge flared gold, solidifying beneath them. Lyra raised an eyebrow. "Quick. But fractions are just the start. The Tower's digging deeper now."
As they reached the arch, a new problem appeared, carved in blue light:
Simplify: (4/5) ÷ (2/3)
Mark visualized it. Dividing fractions meant multiplying by the reciprocal. So, 4/5 × 3/2 = (4 × 3)/(5 × 2) = 12/10 = 6/5.
"Six fifths," he said.
The arch parted, revealing a circular chamber with walls of spinning gears, each engraved with numbers. Numen swirled around Mark, lighter now, like a breeze carrying possibility. But Lyra's expression darkened. "You're good with numbers," she said. "But the next test isn't just math. It's trust."
The Chamber of Exponents
The gears on the walls clicked, forming a new problem in blazing red:
Simplify: 2³ × 2²
Mark's mind raced. Exponents were power, growth—Numina's scholars used them to amplify Numen in rituals. Same base, so add the exponents: 2³ × 2² = 2^(3+2) = 2⁵ = 32.
"Thirty-two," he said.
The gears spun faster, and a platform rose from the floor, lifting them toward a ceiling that shimmered like a starry sky. But as they ascended, Lyra grabbed his arm. "Listen," she hissed. "The Tower's alive, and it's not kind. That choice you made—negative four—it marked you. The next problem might ask for more than an answer."
"What do you mean?" Mark asked, his voice tight.
She didn't answer. The platform stopped, and a final problem appeared, written in light so bright it hurt to look at:
Solve: 4^x = 64
Mark's breath caught. He knew 64 was a power of 4: 4¹ = 4, 4² = 16, 4³ = 64. So, x = 3.
"Three," he said, but his voice wavered. The air grew heavy, and the chamber shook. The light twisted, forming a figure—a shadow with eyes like burning equations. It spoke:
"You wield numbers well, Mark of Numina. But power demands sacrifice. To pass, give us a piece of yourself."
Mark froze. Lyra stepped forward, her Seal glowing faintly. "Don't," she whispered. "Not yet."
The shadow's eyes narrowed, and the chamber began to collapse, gears grinding, walls cracking. Mark's chalk trembled in his hand. He had to decide—now.