Day 12: The Ultimate Supply Chain Test
Act II: Debugging the Supply Chain - FINALE
Location: Speicherstadt Coordination Center
It’s late evening. Frau Weber’s team has been working around the clock to prepare the warehouse distribution systems for final activation. Presents are organized, routes are planned, and delivery vehicles are ready.
But there’s one final obstacle.
The central coordination terminal—the master system that synchronizes all three warehouses and controls the actual distribution to Hamburg’s Christmas markets—remains locked. The screen glows an obnoxious shade of green as the Grinch appears, looking irritatingly well-rested.
System Message from CEO
“Well, well. Day 12. Halfway through your little crusade. Congratulations on making it this far. I’m genuinely surprised—I had a bet with my personal assistant that you’d give up by Day 8. I owe her a very expensive coffee machine now.
Let me be clear about what’s at stake: This terminal controls the ACTUAL distribution of presents to Hamburg’s markets. Not theoretical presents. Not warehouse-locked presents. Actual, physical, needs-to-move-before-Christmas presents.
The locks? They’re application problems. The kind where mathematics meets the real world and most students realize they should have paid attention in class.
Exponential functions. Mixture calculations. Integer optimization.
This is where equations stop being academic exercises and start being the difference between Christmas happening or not happening.
No pressure. Except all the pressure.”
– GR
The Challenge
Three complex, real-world problems stand between you and the complete restoration of Hamburg’s supply chain. The Grinch has labeled them with his signature lack of modesty.
Lock 1: “The Logistics Nightmare”
A supply train carrying essential Christmas materials is running late. Its distance traveled \(D\) (in miles) is given by a function that combines exponential and linear components:
\[D(t) = 50 \cdot 2^{t/3} + 20t\]
where \(t\) is time in hours since departure. The train must reach \(D = 320\) miles to arrive at Hamburg Hauptbahnhof on time.
Grinch’s Note: “This equation doesn’t solve nicely with algebra. You’ll need to test integer values. I know, I know—trial and error feels beneath you. Welcome to real engineering, where elegant solutions are a luxury.”
Determine the time \(t\) when the train reaches exactly 320 miles. Test integer values.
Lock 2: “The Chemistry Department’s Revenge”
The warehouse’s climate control system needs antifreeze for the heating units before they can safely distribute temperature-sensitive presents.
Current Situation:
- Existing solution: 10 liters at 20% antifreeze concentration
- Required concentration: 50% antifreeze
- Available: Pure antifreeze (100% concentration)
Grinch’s Note: “Mixture problems. The bane of every student who thought ‘I’ll never use algebra in real life.’ Spoiler: you will. Frequently. Usually when the stakes are highest.”
How many liters of pure antifreeze must be added?
Enter the amount (in liters):
Lock 3: “The Integer Inquisition”
The warehouse’s final security lock is a classic integer puzzle embedded in the route optimization system:
Authentication Riddle:
“The product of two consecutive positive integers is 72. Enter the LARGER of the two integers.”
Grinch’s Note: “I could have made this harder. I could have used three consecutive integers, or asked for the sum of squares, or required you to prove uniqueness. But it’s Day 12 and I’m feeling generous. Don’t get used to it.”
Enter the larger integer:
Status Update
You work through each problem methodically:
- Train arrival: \(t = 6\) hours (verified: \(50 \cdot 2^{6/3} + 20(6) = 50 \cdot 4 + 120 = 320\) ✓)
- Antifreeze needed: 6 liters (verified: \(\frac{2 + 6}{10 + 6} = \frac{8}{16} = 50\%\) ✓)
- Consecutive integers: 8 and 9 (verified: \(8 \times 9 = 72\) ✓)
You input the final answer. The terminal processes for what feels like an eternity. Then:
FINAL AUTHORIZATION: GRANTED
SUPPLY CHAIN COORDINATION SYSTEM: UNLOCKED
DISTRIBUTION TO CHRISTMAS MARKETS: ENABLED
Every screen in the coordination center lights up with green status indicators. Distribution routes activate. Delivery schedules populate. The entire supply chain—from warehouses to markets—is finally operational.
Frau Weber pulls up a map of Hamburg on the main screen. Green markers appear at every Christmas market location: Rathausmarkt, Jungfernstieg, Mönckebergstraße, Großneumarkt.
“We can start deliveries tomorrow,” she says, her voice thick with emotion. “The markets can physically reopen.”
A message appears on screen. The Grinch’s expression is… complicated. Annoyed, certainly. But maybe something else underneath.
#status-update
“Fine. You win the supply chain.
Current Status:
- ✓ Warehouses: Permanently unlocked
- ✓ Presents: 15,000 units freed
- ✓ Distribution: Fully operational
- ✓ Delivery routes: Optimized
You’ve proven you can handle applied mathematics. Real-world problems. Logistics under pressure.
But here’s what you STILL haven’t done: You haven’t proven Christmas makes ECONOMIC sense.
My business model says Christmas is financially inefficient. Negative ROI. Measurable waste. I presented this analysis to the Hamburg City Council, and mathematically? I was convincing.
Days 13-17: Functions as Business Models.
You’re moving to Europa Passage. You’re going to analyze profit functions, cost curves, and optimization problems. You’re going to prove—mathematically—that Christmas markets are economically viable.
The supply chain is yours. But the economy? That’s still mine.
See you in the business district.”
– GR
ACT II: SUPPLY CHAIN DEBUGGING - COMPLETE ✓
Major Achievements:
- ✓ All three warehouses permanently unlocked
- ✓ 15,000 presents freed from lockdown
- ✓ Emergency failsafes deactivated
- ✓ Re-encryption protocols cancelled
- ✓ Distribution system fully operational
ACT III: BUSINESS MODEL ANALYSIS - Begins Tomorrow
Next Challenge: Prove Christmas is economically viable
Time Remaining: 12 days until Christmas Eve