Airplane riddle: How many airplanes needed for one plane to fly around the world?
Airplane Riddle of Flying Around the World: One airport can be used by airplanes. An airplane carries enough fuel to fly halfway across the globe...
A number of airplanes are available for instant flight on a solitary airport. Airplanes take flight from and land on only this solitary airport.
Each plane can hold just enough fuel to take it halfway across the world. Any amount of fuel that is needed can be transferred from one plane to another while the planes are in flight.
Refueling in flight or at ground as well as turning back of a plane in flight takes no time.
The only source of fuel is on the island.
Dream of flying around the world: One plane is to fly around the world in a great circle.
With zero take-off and landing time, same constant speeds and constant fuel consumption rates, what is the minimum number of planes needed to fulfill the dream with all planes returning safely back to the single airport?
Time to find a way to make one plane fly around the world using minimum number of planes, minimum amount of fuel and all planes flying back to their base safely, is 30 minutes.
Give it a good try before going through the solution.
Solution to Airplane riddle of flying around the world: First stage: Precise problem definition
In a project of problem solving you have to,
- Make an exhaustive list of facts that have been stated and UNSTATED in the problem, and,
- Clearly describe the requirements to solve the problem.
For this problem the list of facts stated is,
- Airport for starting flight and landing is ONLY ONE.
- You can acquire enough number of planes and amount of fuel in the single airport base for successful completion of the project.
- Each plane can hold exactly the amount of fuel to fly HALF the distance around the world.
- A plane can take flight, land, about turn or refuel mid-air taking zero time.
What is required: To make a plane fly around the world using minimum number of planes without wasting any fuel and ensuring that all planes used return safely back to their base.
We would jot down down this much as problem definition at this stage.
Solution to Airplane riddle of flying around the world: Second stage: Primary Barrier analysis: Make a trial trip
What makes your job difficult must be known when you start putting your mind to systematically analyze the problem.
To know the difficulty in solving the problem, a natural action is to mentally make a TRIAL TRIP using two planes at first.
The plan is to see,
- What maximum amount of fuel can be transferred from Plane 2 to Plane 1 for mid-air refueling, and,
- How far can the two planes fly together before Plane 2 MUST REFUEL Plane 1 mid-air and start its flight back for safely reaching the base.
Immediate conclusion made as answer to these questions is,
Conclusion 1: For safely returning to the base, Plane 2 can transfer fuel to Plane 1 to the tune of maximum of half of its full-tank capacity. Half-tank left would be just enough fuel for the Plane 2 return back to base.
So using half of full-tank fuel, Plane 2 can fly with Plane 1 only ONE-FOURTH of the full distance around the world.
What happens at this ONE-FOURTH point after refueling?
Plane 1 tank becomes full, and it would be able to fly an additional half of the distance around the world, that is, a total distance of THREE-FOURTHS of the distance around the world.
This is the maximum that can be achieved with only two planes used.
Conclusion 2: Three planes at the least are required for making one plane fly around the world with all conditions satisfied.
Question is: Would it really be possible even if you use three planes? And if possible, how?
You set down again to mentally visualize three planes flying together from their base. At the one-fourth point Plane 2 refuels Plane 1 with half-tank fuel and returns back to base.
What would then the third plane do?
- At one-fourth point, it CANNOT transfer ANY FUEL to Plane 1 as tank of Plane 1 is already full.
- It is unable fly further on as in that case it would obviously be short of fuel to return.
This is the first real barrier you face. Go on to increase the number planes, but the barrier would remain unbreached if you think in this way.
It's clear that thinking this way won't do.
Naturally. For solving any good riddle you must think new, think innovative.
At this point you stop for a moment and start looking for possibilities that you might have missed.
Solution to Airplane riddle of flying around the world: Third stage: You realize that world is round
With pressure on for thinking of new possibilities, in a flash of revelation you realize that THE WORLD IS ROUND,
A third plane can easily start from the single airport BUT IN OPPOSITE DIRECTION to meet the Plane 1 at the one-fourth point in the opposite direction.
The simple and elegant OTHER WAY ROUND solution falls in place,
- Plane 1 and Plane 2 take flight together in forward direction.
- At one-fourth point in FORWARD DIRECTION, Plane 2 refuels Plane 1 with half-tank fuel to make tank of Plane 1 full.
- With half-tank fuel left, Plane 2 would to the base safely and Plane 1 would fly on. It would reach maximum up to the three-fourth point in FORWARD DIRECTION when its fuel would get exhausted.
- With communication from plane to ground in place, Plane 3 takes flight from base at the right time but in the REVERSE DIRECTION of flight just as Plane 1 reaches halfway mark. At the same time Plane 2 lands safely.
- Plane 3 meets Plane 1 at the one-fourth point of the REVERSE DIRECTION, that is the three-fourth point in the FORWARD DIRECTION.
- Plane 3 refuels Plane 1 with half-tank fuel, and with half-tank fuel in each both planes fly to the base safely.
Success! Plane 1 has flown around the world and the minimum number of planes are used with full safety in the whole project.
A schematic of the successful flights is shown.
This is a good example of how an inventive principle, the Other way round principle, helps to solve a tricky problem.
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