Given a positive integer n, a collection S of n−2 unordered triples of integers in {1,2,…,n} is n-admissible if for each 1≤k≤n−2 and each choice of k distinct A1,A2,…,Ak∈S we have ∣A1∪A2∪⋯Ak∣≥k+2.
Is it true that for all n>3 and for each n-admissible collection S, there exist pairwise distinct points P1,…,Pn in the plane such that the angles of the triangle PiPjPk are all less than 61∘ for any triple {i,j,k} in S?Ivan Frolov, Russia geometrycombinatoricslinear algebracombinatorial geometryRMMSets