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:
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:
How big must N be for this to be possible?
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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