sum of pairwise distances is decreasing
Source: All-Russian Olympiad 1996, Grade 11, First Day, Problem 2
April 19, 2013
geometry proposedgeometry
Problem Statement
Several hikers travel at fixed speeds along a straight road. It is known that over some period of time, the sum of their pairwise distances is monotonically decreasing. Show that there is a hiker, the sum of whose distances to the other hikers is monotonically decreasing over the same period.A. Shapovalov