MathDB

3

Part of 1972 IMO Longlists

Problems(1)

Translating n points so that none remain on the segments

Source:

11/3/2010
On a line a set of segments is given of total length less than nn. Prove that every set of nn points of the line can be translated in some direction along the line for a distance smaller than n2\frac{n}{2} so that none of the points remain on the segments.
geometry unsolvedgeometry