This is a fun little riddle I was hoping to share with all of you since I cannot seem to crack it. I was talking to my friend the other day and he mentioned that the US is capable of bombing any point on earth in at least 22 minutes. He estimated the velocity of these bombers to be about 5,000 mph. Whether these figures are true or realistic is somewhat irrelevant to me, whatever the true numbers are, I became curious as to how you would go about calculating the fewest number of planes possible to satisfy these conditions.
Assuming we're not accounting for take-off, landing, or other factors, each plane would be capable of flying anywhere within a circle of radius 1833.33 miles in that time frame. Below is an image I mocked up of what I believe would be the most efficient way to distribute those areas (the planes being at the center of each circle), so that all points can be traversed.
Now if Kyrie Irving and Shaq were right and the world were a a flat 2d plane, I think the answer would be fairly trivial from here... circumscribe the pattern in the picture above within its bounds... but being that the earth is a sphere, let's just say a perfect sphere with a circumference of 24,901 miles, - I'm not sure how to approach this. I haven't thought much about non-euclidian geometry since high school, and I'm not sure how what I do remember might apply.
Thanks! Interested to hear your ideas!
I'm sorry to tell you, but with a more realistic speed for the planes the world is flat, or it might as well be. A more realistic speed for the bombers is $1000$ mph, which is about right for the US B-58 supersonic bomber. That gives a range of only $367$ miles in $22$ minutes. The curve of the earth will not be important, so just figure the area of $\pi 367^2 \approx 423,000$ square miles per plane compared to an earth surface area of $\pi 24901^2$ and multiply by $4/3$ for overlap of the circles, giving that you need $6138$ planes to cover.