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Part of 1980 Czech And Slovak Olympiad IIIA

Problems(1)

min no of convex sets whose union is M (plane - 3 vertices of triangle)

Source: Czech and Slovak Olympiad 1980, National Round, Problem 3

9/13/2024
The set MM was formed from the plane by removing three points A,B,CA, B, C, which are vertices of the triangle. What is the smallest number of convex sets whose union is MM?
[hide=original wording] Množina M Vznikla z roviny vyjmutím tří bodů A, B, C, které jsou vrcholy trojúhelníka. Jaký je nejmenší počet konvexních množin, jejichž sjednocením je M?
combinatoricscombinatorial geometrygeometryConvex Set