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MMO 181 Moscow MO 1950 polygons by all diagonals in 1950-gon

Source:

August 6, 2019
geometrycombinatorial geometryconvex polygondiagonals

Problem Statement

a) In a convex 1313-gon all diagonals are drawn, dividing it into smaller polygons. What is the greatest number of sides can these polygons have?
b) In a convex 19501950-gon all diagonals are drawn, dividing it into smaller polygons. What is the greatest number of sides can these polygons have?