Subcontests
(4)Convex polygons
For a given positive integer n>2, let C1,C2,C3 be the boundaries of three convex n− gons in the plane , such that
C1∩C2,C2∩C3,C1∩C3 are finite. Find the maximum number of points of the sets C1∩C2∩C3. Many square roots, but rational !
Find all positive integers n such that there exist a permutation σ on the set {1,2,3,…,n} for which
σ(1)+σ(2)+…+σ(n−1)+σ(n)
is a rational number.