A number theory problem by Anik Mandal

.A fly is being chased by three spiders on the edges of a regular octahedron. The fly has a speed of \(50\) meters per second, while each of the spiders has a speed of \(r\) meters per second. The spiders choose the (distinct) starting positions of all the bugs, with the requirement that the fly must begin at a vertex. Each bug knows the position of each other bug at all times, and the goal of the spiders is for at least one of them to catch the fly. What is the maximum \(c\) so that for any \(r < c\), the fly can always avoid being caught?

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