Okay, we have a solution for the plane. The plane is in two dimensions. Now, for any positive integer n, generalize the problem to n dimensions. So, now the

Okay, we have a solution for the plane. The plane is in two dimensions. Now, for any positive integer n, generalize the problem to n dimensions. So, now the problem is, for any positive integer n, given any 2^n + 1 n-tuples of integers, at least two of these n-tuples if added have all even components.