369

Part of 1983 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 369 All Soviet Union MO 1983 k non-intersecting segments in set M

Source:

M

set consists of

k

non-intersecting segments on the line. It is possible to put an arbitrary segment shorter than

1

cm on the line in such a way, that his ends will belong to

M

. Prove that the total sum of the segment lengths is not less than

1/k

Segmentcombinatorial geometrygeometry