Hint to Riddle #79: Flatland Airports

79. -Flatland is a plane extending infinitely in all directions. It has an infinite number of airfields no two of which are exactly the same distance apart.

-At a point in time a plane will take off from each airport and land at it's nearest neighbouring airport.

-What is the maximum number of aeroplanes that may land at any single airfield?
boggs euromorphic projection of the flat earth Let's get an idea of the set up:

a map of flatland with the airports randomlyplaced and arrows showing the flight of a plane to it nearest neighbouring airport.

So the airports (blue dots,) are spread about randomly an aeroplane will travel from it to the nearest neighbouring airport. Down in the bottom right we can see an airport with three aeroplanes arriving...

I think it's easy enough to see where an extra airport could be added so as to increase that to four. But at some point with an additional airport it's nearest neighbour would change to being the ones you've added and no the original.

That limit is the answer to the question.

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