Given a positive integer n, a set S is n-admissible if

①each element of S is an unordered triple of integers in {1,2,⋯,n},

②|S|=n-2,and

③for each 1≤k≤n-2 and each choice of k distinct A₁,A₂,⋯,A_k∈S,

|A₁∪A₂∪⋯∪A_k |≥k+2

Is it true that, for all n>3 and for each n-admissible set S, there exist pairwise distinct points P₁,P₂,⋯,P_n in the plane such that the angles of the triangle P_i P_j P_k are all less than 61° for any triple {i,j,k} in S?

【译】给定正整数n，称集合S是n-可行,如果其满足以下条件：

①S的每个元素都是{1,2,⋯,n}的三元子集；

②|S|=n-2；

③对任意的1≤k≤n-2和任意k个互不相同的A₁,A₂,⋯,A_k∈S，都有

|A₁∪A₂∪⋯∪A_k |≥k+2

判断以下命题是否为真：对所有n>3和所有的n-可行集合S，在平面内总存在n个互不相同的点P₁,P₂,⋯,P_n，使得对集合S中任意元素{i,j,k}，三角形P_i P_j P_k的每个内角都小于61°.