This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 3

Novosibirsk Oral Geo Oly IX, 2019.6
Tags: polyline , geometry
A square with side $1$ contains a non-self-intersecting polyline of length at least $200$. Prove that there is a straight line parallel to the side of the square that has at least $101$ points in common with this polyline.

1978 Chisinau City MO, 163
Tags: geometric inequality , geometry , polyline , point , combinatorial geometry
On the plane $n$ points are selected that do not belong to one straight line. Prove that the shortest closed path passing through all these points is a non-self-intersecting polygon.

2019 Novosibirsk Oral Olympiad in Geometry, 6
Tags: geometry , polyline
A square with side $1$ contains a non-self-intersecting polyline of length at least $200$. Prove that there is a straight line parallel to the side of the square that has at least $101$ points in common with this polyline.