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Assume that the galaxy is a large cube, made up of 200 billion stars, each star positioned on the corner of a small cube arranged together in a lattice. The entire lattice of small cubes makes up the larger cube representing the entire galaxy. Let the distance between each neighboring star be D = 5 LY, where D is the length of the side of one of the small cubes. If 100 currently signaling civilizations are randomly distributed somewhere in this 'cubic' galaxy, how far away in LY is the nearest civilization likely to be?

There was an answer to this problem already posted on course hero, but I did not understand how to get the answer.

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