MathDB

A spherical planet has the equator of length

1

. On this planet,

N

circular roads of length

1

each are to be built and used for several trains each. The trains must have the same constant positive speed and never stop or collide. What is the greatest possible sum of lengths of all the trains? The trains are arcs of zero width with endpoints removed (so that if only endpoints of two arcs have coincided then it is not a collision). Solve the problem for : (a)

N=3

(4 points) (b)

N=4

(6 points)
Alexandr Berdnikov

Problem Statement