# Microsoft interview questions [question] aircraft refueling problem

CSDN University Club Interview questions Microsoft

Liang wood water Chen

graduateBeijing University of Posts and Telecommunications

Known:

Each plane has only one oil tank, the aircraft can be mutual refueling (note that each other, there is no tanker). A box of oil can be used for a plane to fly around the earth.

Question:

At least a few planes are required to make at least one plane return to take off at the airport. All planes take off from the same airport, and must return safely to the airport, not allowed to land in the middle of the airport.

Our calculation results: a total of 5 sorties dispatched to complete the mission.

If you perform this task, you will send a few flights?

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2014-12-12
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2015-09-08
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Liang wood water Chen

graduateBeijing University of Posts and Telecommunications

Choose 3 more students, is not the two planes did not consider the return, the 1/2 box oil added to other aircraft? To pay attention to the requirements of the subject,All aircraft fromSame airportTake off, and have toSafe return to the airport, do not allow to land, there is no airport in the middle.

December 14, 2014 21:47:24

Yuyang199

Why don't you three? Two flew back to the airport can fill up and then fly to pick up this three aircraft that can be done

December 15, 2014 15:43:22

Mo 1103137684

studentNanjing University of Technology

Please read the questions again, he said, is the aircraft sorties. Not a few

December 15, 2014 17:27:23

Cute dog

4 is not it? First three planes in the same direction off, 1 / 3 to run out of the mailbox, the two planes to the third frame respectively, plus 1 / 3 of the oil, and then return to the two planes, the third aircraft continue to fly, the third aircraft to fly soon after a circle, the fourth aircraft deployed to meet, to the third aircraft flying machine with 1 / 3 oil, return and the four aircraft, the third aircraft just can turn a complete circle.

December 21, 2014 15:13:45

Liang wood water Chen

graduateBeijing University of Posts and Telecommunications

Three aircraft flew 1/3 after each aircraft 1/3 empty tank. Second aircraft and third aircraft is not the same time will be 1/3 of the oil to the first aircraft, because the first aircraft fuel tanks can only accept 1/3 of the oil.

December 21, 2014 22:04:16

Vector_change

In order to oil the most province that is sent by the least number of aircraft, 1 machine must walk alone half of the earth.

Then, since the initial state of a half earth is full of oil, and the final state is depleted (critical point).

It must be filled with aircraft 1 aircraft to fill in the first half of the earth when the fuel consumption, the same reverse the aircraft must give enough to return to the origin of the amount of oil 1.

So the next thing to consider is how much the number of additional aircraft that the half earth has led to the start of the 1.

Apparently, the fuel consumption of the half of the earth's 1 aircraft is a burden on other aircraft while other aircraft need to return to the airport so

(1 with the same direction of the fuel consumption of *3 + 1 reverse fuel consumption *3).. (No. 1 with the fuel consumption + 1 reverse fuel consumption) = half of the earth's fuel consumption

This is not to consider the theory of the number of times the minimum number of the theory that the least 3+1 tanks have to have.... Should be the 5 aircraft is not wrong, it is not possible to be less than the 3,4 frame.

The proof is not over yet.... That little show, you do not spray the great God, if there is an error, please enlighten

December 22, 2014 13:19:42

Lxy54101

Three planes

Set up three aircraft for the ABC

ABC took off at the same time, fly to the semi circle of a quarter of a to BC tank, and then return. BC to fly forward, fly to a B C fill spontaneously after return. This is the time to make B as much as possible for the C gas, so B C gas after return to from the starting third of fuel consumption as (because then let a and to reinforce the B, and the longest collusion distance away from the starting point for a third one), you can set B and fly forward distance x C gas and then return to the equation 2x+ (1/4+x-1/3) = 1

Seek x=13/36, namely in 1/4+13/36=11/18 B C fill spontaneously after the return, so C to fly half an earth arrived on the other side of the distance from the starting point of less than a quarter of a point, then the use of AB can be used safely C back to the airport.

Note: the above calculation of the scores, all with a half circle of 1 Calculation

December 22, 2014 16:35:02

Liang wood water Chen

graduateBeijing University of Posts and Telecommunications

What is a few planes. Indeed, a total of 3 aircraft to complete the task, from the current point of view, at least need to be deployed 5SortiesThe aircraft can achieve 3 aircraft by turns.

December 22, 2014 16:54:55

Mine, Cheng Zi

studentOccupation of Tianjin City

5, just want to say 3 children: the plane is only one fuel tank, can not add two boxes of oil,

December 25, 2014 21:50:33

Cute dog

Oh, wrong, I'm sorry.

December 28, 2014 16:11:49

Liang wood water Chen

graduateBeijing University of Posts and Telecommunications

Don't be shy, to discuss the issue should dare to show their own point of view, this will know that is right or wrong. Say your idea is good.

December 30, 2014 14:57:08

Zowa13

studentJiujiang University

That one only 1/3, the other two each to it 1/3, that is 2/3, the tank can not hold so much.

December 31, 2014 17:05:14

Modiz

studentHunan University of Technology

Egg pain forget, considering the aircraft can not reverse the fly situation, calculated the 14. At the beginning of 8 aircraft to fly, each time the fuel consumption of 1/3 gas half home... Then ready to pick up... Orz...

January 3, 2015 11:10:43

Snailssss

studentShanghai second industry

Consider 1/3 after the need to find 6 1/4 also need 6 (number of units behind the box / oil is also omitted)

To make one of the aircraft around the earth to fly a circle back to the airport, to remove the province's 1, but also requires 1 of the oil

Out of plane

It is not difficult to understand, the plane II, the use of 1/4, the 1/4 to the first II, II of the 1/4 to the third, back, and continue to fly. At this time, there are 1 of the oil. (the oil is still poor 3/4)

The plane continued to fly 1/4, the plane of the 1/4 to the first, and the rest of the 1/2 back, at this time, there are 1 of the oil, (also sent 1/2)

At this time of the 5 6 back from the airport, flying 1/4, 4 1/4 to 5, 4 1/4 to 6, 5, 6, the 1 oil,

The 6 1/4 met separately and then fly to 1/4 to such 1 will meet the back of oil.

The use of 1/3 is also required to consider 6, please explain how the 5 is out of the?

Can not figure.

January 6, 2015 20:21:58

Snailssss

studentShanghai second industry

Know, 45 out of the time did not think clearly, hey, good stupid, began to see the answer, thinking that the landlord to let us think, after the refresh found that there is an answer.. Just understand.

January 6, 2015 20:31:40

Liang wood water Chen

graduateBeijing University of Posts and Telecommunications

The 8 aircraft flying is what happens? Why do you want to fly so many planes at the same time?

January 7, 2015 11:38:32

Liang wood water Chen

graduateBeijing University of Posts and Telecommunications

Through their own thinking to understand, where there is stupid to say.

January 7, 2015 11:40:23

Modiz

studentHunan University of Technology

In order to ensure that there is a fly ash fly half of the distance or to ensure that the state of full oil...

January 12, 2015 13:41:40

Liang wood water Chen

graduateBeijing University of Posts and Telecommunications

Drawing a diagram to illustrate the idea?

January 12, 2015 16:10:23

Modiz

studentHunan University of Technology

January 14, 2015 00:14:51