2016 Latvia National Olympiad 3rd Round Grade10Problem5
Source:
July 22, 2016
geometrycombinatorics
Problem Statement
All vertices of a regular 2016-gon are initially white. What is the least number of them that can be painted black so that:\\
(a) There is no right triangle\\
(b) There is no acute triangle\\
having all vertices in the vertices of the 2016-gon that are still white?