The main resemblance of all the hardest hard riddles is that they all seem very difficult and unsolvable, but when you read the solution, you'll feel sorry and think that you should be able to find the answer at the first place.
This time hardest riddle, "How Many Planes?", is probably the same too. Just try to use your logic and little math to solve this one, and think thoroughly before giving up, as you'll find that this puzzle is actually can be solved quite easily.
So, here goes:
On a secret island, there is an lab and airport conducts a research of some new generation of airplanes. Now the airport is the home base of an unlimited number of identical airplanes. Each airplane has a fuel capacity to allow it to fly exactly 1/2 way around the world, along a great circle.
The planes have the ability to refuel in flight without loss of speed or spillage of fuel. Though the fuel is unlimited, the island is the only source of fuel.
Question: What is the fewest number of aircraft necessary to get one plane all the way around the world assuming that all of the aircraft must return safely to the airport? Explain your answer!
Notes:
- Each airplane must depart and return to the same airport, and that is the only airport they can land and refuel on ground.
- Each airplane must have enough fuel to return to airport.
- The time and fuel consumption of refueling can be ignored. (so we can also assume that one airplane can refuel more than one airplanes in air at the same time.)
- The amount of fuel airplanes carrying can be zero as long as the other airplane is refueling these airplanes.
Difficulty:
