The puzzle question is : On Bagshot Island, there is an airport. The airport is the homebase 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.
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? How did you get to your answer?
Notes:
(a) Each airplane must depart and return to the same airport, and that is the only airport they can land and refuel on ground.
(b) Each airplane must have enough fuel to return to airport.
(c) 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.)
(d) The amount of fuel airplanes carrying can be zero as long as the other airplane is refueling these airplanes. What is the fewest number of airplanes and number of tanks of fuel needed to accomplish this work? (we only need airplane to go around the world)
My answer will need six planes (Main Plane included) total.
ReplyDeleteHere are how these will work with three kinds of Plane Flights:
(Notes: One flight will reach half way around the world.
One third (1/3) flight will reach 1/6 around the world.)
1) Mission plane will fly all the way around the world.
This plane will get refueled by other planes along the way.
2) One-third (1/3) Plane - this plane will fly 1/3 distance.
Then the plane will fuel other plane 1/3 and fly back 1/3.
3) Two-third (2/3) Plane - this plane will fly 2/3 max distance.
The plane will get refueled 1/3 at 1/3 distance both ways.
Then the plane give the Mission plane 1/3 fuel.
The flights sequence will be lined up as follows:
1) Mission Plane will fly first. (1st Plane)
2) Two-third Plane will fly the same time. (2nd Plane)
3) Mission Plane will get refueled by the first 1/3 Plane. (3rd Plane)
The first 1/3 plane will fuel the Mission Plane 1/3 tank and back.
4) Two-third Plane will also get refueled by second 1/3 Plane. (4th Plane)
The second 1/3 plane will fuel the Two-third Plane 1/3 tank and back.
5) Two-third Plane will refuel 1/3 tank to Mission Plane at 2/3 distance.
6) Two-third Plane will also get refueled by third 1/3 Plane. (5th Plane)
The third 1/3 plane will fuel the Two-third Plane at 1/3 point and back.
7) The Mission Plane will then have 5/3 of fuels to have 1/3 tank short.
The last 1/3 plane will fuel the Mission Plan on the way back. (6th Plane)
Now the Mission Plane will have enough fuels to fly back.
Mmm... you are not correct sorry :(! posting the answer up on the answer site now though to upload the new riddle :)
Deleteif a flight can go halfway around the world it can be refilled to full tank at a quarter of the way using 3 other planes, the same 3 planes can be reused to refuel it at 3/4 of the way. (the fueling planes go 1/8 of the world before one of them shares half of its full tank between the other two planes.)
ReplyDeleteI reached this answer by asking how I could get half a tank refilled on one side so I could do the same on the other side.