MathDB

There is a frog in every vertex of a regular 2n-gon with circumcircle(

n \geq 2

). At certain time, all frogs jump to the neighborhood vertices simultaneously (There can be more than one frog in one vertex). We call it as \textsl{a way of jump}. It turns out that there is \textsl{a way of jump} with respect to 2n-gon, such that the line connecting any two distinct vertice having frogs on it after the jump, does not pass through the circumcentre of the 2n-gon. Find all possible values of

n

Problem Statement