Problem

Source:

Tags: vector, combinatorics, combinatorial geometry



There are $n > 1$ points on the plane. Two take turns connecting more an unconnected pair of points by a vector of one of two possible directions. If after the next move of a player the sum of all drawn vectors is zero, then the second one wins; if it's another move is impossible, and there was no zero sum, then the first one wins. Who wins when played correctly?