Day 6: The Master Algorithm
Act I: Infiltration - Finale
Location: GrinchTech Executive Suite, Floor 5
The elevator shoots upward, crossing back over the Elbe via an underground tunnel. When the doors open, you’re on Floor 5—the Executive Suite.
It’s minimalist to the point of sterile: glass walls overlooking Hamburg, a single standing desk with multiple 8K monitors, and a massive holographic display showing a 3D model of Hamburg with every Christmas system mapped out in red.
The Grinch stands at the window, silhouetted against the grey December sky. He doesn’t turn around.
“Welcome,” he says, his voice bored. “You’re late. I expected you five minutes ago.”
He gestures to the holographic display. “This is my masterpiece. The Christmas Optimization Platform (COP). Everything you’ve solved so far—number theory, factorization, logarithms—those were just the warm-up. Now let me show you the real complexity.”
The display shifts, showing a massive mathematical expression that combines multiple concepts.
System Message: The Grand Design
“This is the core algorithm. Solve this, and I’ll grant you read-access to the control systems. Fail, and I’ll have security escort you out.
I’ve combined everything. Multi-step expressions. Complex factorization. Radical simplification. Logarithmic equations.
Impress me. If you can.”
– GR
The Challenge
The holographic display presents four interconnected problems.
Task a) System Stability Index
The core algorithm’s stability is determined by evaluating this complex expression. Order of operations is critical. \[[(10 - 2^2) \div 2 + \sqrt{81}] \times \log_5(125)\]
Grinch’s Note: “Everything you’ve learned so far, combined. Brackets, exponents, roots, logarithms. Miss one step and the whole thing falls apart. Like my faith in humanity. Which happened years ago.”
Evaluate:
Task b) Security Key Factorization
The master encryption key is a high-degree polynomial.
\[x^4 - 16\]
Grinch’s Note: “Difference of squares… but wait, there’s more! One of the factors is ALSO a difference of squares. Most people stop too early. Don’t be most people. I’m begging you. Not literally, I don’t beg, but metaphorically.”
Requirement: Factorize completely (do not stop at difference of squares).
Task c) Energy Distribution Formula
The power grid uses a radical expression. Simplify it to restore lighting voltage. \[\frac{\sqrt{18} + \sqrt{50}}{\sqrt{2}}\]
Grinch’s Note: “Radical simplification. Combine like terms under the roots, rationalize if needed. Or just stare at it in confusion—that’s what the last three people did. They work in retail now.”
Simplify:
Task d) Market Activation Code
The final authentication for the market control panel is a logarithmic equation. \[\log_3(y) + \log_3(2) = 2\]
Grinch’s Note: “Log properties. When you add logs of the same base, you’re really… well, if you don’t know, you should have paid more attention.”
Solve for y:
Status Update
You input the final answer: 4.5
The holographic display flashes green. Every number, every equation, every factor resolves into a single word that pulses in the air: AUTHENTICATED.
The Grinch turns to face you. He looks… annoyed. But also slightly respectful.
“Thirty-six. Complete factorization. Eight. Four-point-five.” He says each answer slowly. “All correct. How disappointing. I was hoping to watch security throw you out.”
He taps his standing desk. The red systems on the map flicker to amber.
System Status Update
- Warehouse Access: PARTIAL (read-only)
- Market Controls: LOCKED
- Lighting Grid: LOCKED
- Supply Chain: ACTIVE
“Fine,” the Grinch sighs. “You understand the math. But understanding my systems and dismantling them are very different things. Phase One is complete. You’ve infiltrated my operation. Here is your reward: More work.”
He gestures to the display, where new objectives appear:
Phase Two: System Debugging
“My supply chain algorithms are still running. Presents are locked in Speicherstadt. Automated sorting systems are optimized to keep Christmas canceled.
If you want to restore Hamburg’s holiday, you’ll need to debug my logistics. Days 7-12 will test you in ways the foundations never could.
Good luck. Try not to break anything expensive.” – GR
Act I: Infiltration - COMPLETE