Est. 1998 — 27 years of woodworking knowledge
Friday puzzler -- Moondoes on an island
Alex Y
Round Island is, as you may have guessed, a island that is a flat disk, exactly 20 miles in diameter. Moondoes has decided to put up to seven coffee shops on the island, and wants to position them to minimize the worst-case (longest straight-line) walk from anywhere on the island to one of their shops.
How far can you get from a Moondoes on this island, and how are the shops positioned?
Re: Friday puzzler -- Moondoes on an island
David Weaver
I think I'll call UPS and borrow their logistics software for this one!!
Maybe there's some use for the simplex method in this, but I don't remember anything other than that it exists.
Re: Friday puzzler -- Moondoes on an island
Alex Y
I'm not familiar with the simplex method, but you need no math beyond 9th-grade geometry for this one. 
Re: Friday puzzler -- Moondoes on an island
Bill Earl
There are 6 places on the island where you would have to make a 'trivial' decision.
Alex Y
Took me a while to figure out your meaning for "trivial". Clever!
Answer
Alex Y
Congrats to Bill for getting this one. The coffee shops can be placed so that anywhere on the island is within five miles of one of the shops. One shop is at the center of the island. For the other six, inscribe a hexagon in the circle defining the island's shore, and put a coffee shop at the center of each edge of this hexagon.
The six "trivial" as in "tri-value" points Bill referred to are the midpoints of the radii going to the vertices of the hexagon. These points are 5 miles from the center and from the center of the two neighboring edges.