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How many pilots do they need?

Puzzling Asked by Matheinstein on July 14, 2021

I have just watched this old riddle video from Ted-Ed. It basically asks how can three pilots coordinate their flights such that the professor (one of the three pilots) can circumnavigate the earth. I would recommend you watch the video before answering this question. The question is: If the planes were to only hold 90 kiloliters of fuel, how many pilots would they need to allow the professor to circumnavigate the earth. I do not know the number, nor do I know if it is even possible.

Summarised rules of the original problem:

Rules

And rules for this problem is as follows.

N pilots, one of them is our professor, want to circumnavigate the earth (360 longitudinal degrees) with the following conditions:

  1. Professors plane cannot turn/land (must be continuous)
  2. Each plane travels 1deg/min using 1kL fuel in the process. Each plane has 90kL fuel capacity.
  3. Refueling can be done in either at airport or between planes. Refueling is instant and the two planes must be at the same position for fuel transfer to happen.
  4. All refuelers can turn around instantly (but not the professor’s, see rule 1)
  5. Refuelers cannot crash; all must land on the airport.

How big must N be for this to be possible?

3 Answers

Temporarily scrapping this partial idea as I found a better solution, but will leave it here to inspire others.

Essentially the strategy is

I say this because

Working backwards is the best way to do this:

Step 1:

Step 2:

Answered by Ankit on July 14, 2021

As pointed out by @loopy wait, this answer is wrong. Just leaving it up here for inspiration.

The answer is

Corridor Property:

Sustainance property:

Starting the main plane:

Retriving the refuelers:

Recieving the plane:

The final stretch:

I apologise this is really confusing to read. I will try to make an animation soon, but I am very busy with school atm.

Answered by Ankit on July 14, 2021

I believe that it takes a minimum of

To do this, we rely on a range of alternate refueling steps.

Using these strategies, as illustrated in the fairly self-explanatory diagram below, the circumnavigator can complete a trip that includes flying a 90 degree solo leg with refueling at both ends of that section of the trip. I believe that this solution not only uses the minimum number of pilots, but also uses the minimum quantity of fuel. Note that in the diagram, one or more re-fueling events (as described above) occurs at every intersection of two 'flight-lines'.

Answered by Penguino on July 14, 2021

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