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251

Part of 1953 Moscow Mathematical Olympiad

Problems(1)

MMO 251 Moscow MO 1953 2 groups of convex polygons from 16 concyclic points

Source:

8/9/2019
On a circle, distinct points A1,...,A16A_1, ... , A_{16} are chosen. Consider all possible convex polygons all of whose vertices are among A1,...,A16A_1, ... , A_{16} . These polygons are divided into 22 groups, the first group comprising all polygons with A1A_1 as a vertex, the second group comprising the remaining polygons. Which group is more numerous?
pointscircleconvex polygoncombinatorial geometry