The Airplane Riddle: A Fuel-Efficient Flight Around the World

Professor Fukanō, a brilliant scientist and adventurer, has set his sights on an ambitious goal: a nonstop, round-the-world flight in his uniquely designed aircraft. However, a significant challenge looms – the plane's fuel capacity is only sufficient for half the journey. Undeterred, the professor devises a clever solution involving two additional planes to provide crucial mid-air refueling. Can you solve this intricate puzzle and help the professor achieve his dream without anyone running out of fuel?

The Challenge: Circumnavigating the Globe

The professor's plane boasts an impressive speed, capable of traversing one degree of longitude around the equator every minute. This translates to a six-hour journey to complete a full circle around the globe. The catch? The plane's fuel tank can only hold 180 kiloliters, enough for precisely half the trip.

The Professor's Ingenious Solution

Instead of simply increasing the fuel capacity, the professor opts for a more complex approach: utilizing three identical planes. These planes possess remarkable capabilities:

• Exceptional Maneuverability: They can execute swift turns.
• Mid-Air Fuel Transfer: They can instantly transfer fuel to each other during flight without losing speed.

The professor will pilot the primary aircraft, with his assistants, Fugōri and Orokana, piloting the other two.

The Constraints

The experiment faces certain limitations:

• Single Airport: Only one airport, situated on the equator, is authorized for takeoffs, landings, and refueling.
• Coordinated Flight: The three planes must coordinate their movements precisely to ensure the professor's success without any crashes.

Cracking the Code: The Optimal Flight Plan

The key to solving this puzzle lies in maximizing the support provided by the assistant planes, ensuring no fuel is wasted. Symmetry plays a crucial role, enabling shorter trips in either direction while setting the stage for a long, unsupported stretch for the professor.

The Step-by-Step Solution

1. Departure: All three planes take off westward at noon, each carrying a full load of 180 kiloliters of fuel.
2. First Refueling Point (1/8th of the way): After 45 minutes, each plane has 135 kiloliters remaining. Orokana transfers 45 kiloliters to both the professor and Fugōri, fully refueling them. Orokana then returns to the airport with her remaining 45 kiloliters.
3. Second Refueling Point (1/4th of the way): Another 45 minutes pass, and the professor and Fugōri each have 135 kiloliters again. Fugōri transfers 45 kiloliters to the professor, leaving himself with 90 kiloliters for the return trip.
4. The Professor's Solo Flight: The professor continues alone, while Orokana prepares for her next mission.
5. Orokana's Eastern Ascent: As Fugōri lands and refuels, Orokana takes off eastward.
6. Halfway Point: After 180 minutes, the professor reaches the halfway point with 90 kiloliters of fuel remaining.
7. Rendezvous (3/4th of the way): The professor and Orokana fly towards each other for 90 minutes, meeting at the three-quarter mark. Orokana transfers 45 kiloliters to the professor, leaving them both with 45 kiloliters.
8. Fugōri's Rescue Mission: Fugōri, having refueled, takes off to meet the other two planes.
9. Final Refueling (315-degree point): After 45 minutes, Fugōri meets the professor and Orokana, transferring 45 kiloliters to each, leaving 45 for himself.
10. Triumphant Return: All three planes land at the airport with empty fuel gauges.

Conclusion: A Triumph of Coordination

Through careful planning and precise execution, Professor Fukanō and his assistants successfully navigate the globe, demonstrating the power of teamwork and ingenuity. This intricate puzzle highlights the importance of resource management and strategic thinking in achieving ambitious goals.